5E - You're Doing It Wrong - Two-Weapon Fighting
A lot of weapons in 5e with the Heavy property also have the Two-Handed property. Which means you can't dual wield them even with the Dual Wielder feat.
- Role Player's Respite (https://roleplayersrespite.com), "Your Simple Guide to Dual Wielding in DnD 5e"
Wielding two weapons is one of those things that looks bad-ass and as a result, players often want to be able to do with their characters. However, the process of actually fighting with two weapons is something of a mixed bag for most classes, and it doesn't make it any easier that many tables get the rules for two-weapon fighting wrong, most significantly, using the rule for two-weapon fighting when it doesn't really apply.
How most characters fight with two weapons
The key rule for fighting with two weapons, for most classes, is found on page 77 of the Player's Basic Rules (or page 195 of the Player's Handbook -- the text is identical):
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
If either weapon has the thrown property, you can throw the weapon in stead of making a melee attack.
First off, some rules explanation. A 'light' weapon is a weapon that has the Light property on the Weapons list on page 48 of the PBR (page 149 of the PH). In fact, the description of the Light property specifically says the weapon is ideal for two-weapon fighting and references the chapter with the rule for Two-Weapon Fighting.
However, one thing folks frequently forget is that the rule also requires that you attack with a 'melee' weapon, which is a weapon listed under 'Simple Melee Weapons' or 'Martial Melee Weapons' on the same list. I have seen a number of charts of 'eligible weapons for two-weapon fighting' that include the hand crossbow (including the linked article in the introductory quote above), because the hand crossbow is a light weapon, but the hand crossbow is not eligible for the rule for two-weapon fighting because it is not a melee weapon, it is a ranged weapon, even when used to make a melee attack. (You can still effectively 'dual-wield' light crossbows, but it requires the use of the Crossbow Expert feat, which contains a variant of the Two-Weapon Fighting rule that allows you to fire a loaded hand crossbow as a bonus action after using the Attack action to attack with a light weapon; note that this variant of the rule does not specify that the initial attack be made with a melee weapon, which enables the use of the light hand crossbow to enable a second hand crossbow attack. However, there is some discussion that this may not allow you to dual-wield hand crossbows for more than a single round, as while the Crossbow Expert feat removes the Loading quality for crossbows with which you are proficient, the feat does not remove the Ammunition property of the hand crossbow, which requires a 'free hand' to reload the crossbow after firing. Holding a hand crossbow in each hand prevents those hands from being considered 'free', based on a similar wording in the spellcasting rules for which the War Caster feat serves as an exception.)
The rule also points out that you use your bonus action to attack with a 'different light melee weapon that you are holding in the other hand', but this does not require that you be using two different kinds of weapons -- you can in fact dual-wield with two daggers, or two scimitars, or two of any identical light weapon, so long as you are actually holding two of them, one in each hand. (The rule effectively prohibits wielding one weapon and simply moving it to your other hand to qualify for the second attack.) In addition, if you have a positive Strength modifier that you would normally add to your weapon damage roll, you do not add this modifier to your damage for your bonus attack. (There are a few other implied restrictions, which we'll cover later when we talk about the rules that allow you to ignore them.)
Note as well that light weapons tend to do less damage than non-light weapons; there is no light weapon on the basic weapon list that deals more than a d6 of damage, while there are a number of 'two-handed' and/or 'heavy' weapons that can deal significantly more than that. This might make some players believe that two-weapon fighting isn't as effective as fighting with one big weapon, but in fact the rules are designed to try to equalize those situations as much as possible for most 'typical' characters. So, for example, say you have two characters with the same Strength score, one of whom is wielding a greatsword while the other is wielding two shortswords. The greatsword wielder will attack once, dealing 2d6+Str damage, while the two-shortsword wielder will attack twice, dealing a total of 1d6+Str+1d6 if she hits with both attacks. This sets up the basic mechanical difference between the two types of fighting: a 'normal' fighter will sometimes miss with a single attack, resulting in no damage, while the dual-wielder, while they will only reach the expected damage of the greatsword fighter if they hit with both attacks, will more frequently hit with at least one attack, resulting in at least some damage.
If you choose to go down the munchkin path, be aware that most optimization sources come to the conclusion that, with the appropriate feats and class options in place, two-weapon fighting is slightly better than great-weapon fighting at low levels, but great-weapon fighting becomes more effective at higher levels, for reasons we're not going to cover in this article. Just be aware that the rule we've already covered applies to all characters, regardless of class, so technically, anybody can fight with two weapons!
How Fighters and Rangers dual-wield
However, as you might expect, some classes are designed to be more effective at fighting with two weapons than others. For the Fighter and Ranger, this comes from the Fighting Style feature that the Fighter gets at level 1 and the Ranger gets at level 2. In each class, one of the options for Fighting Style is this one:
Two-Weapon Fighting
When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack.
This may seem like a fairly tame benefit, but for most low-level characters, not only is this a great bonus, but is the main effect that causes two-weapon fighting to be better than great-weapon fighting at low level. Recall our two-shortsword versus greatsword character from above; if the two-shortsword character has taken the Two-Weapon Fighting fighting style, now that character always does 1d6+Str damage on a hit, regardless of which attack hits, and does 2d6+(Str*2) damage when hitting with both attacks. Since melee fighters tend to have high Strength scores, this means that the two-shortsword character now expects to do more damage overall than the greatsword character.
You may notice that I didn't mention Paladins in this section, even though Paladins also have a Fighting Style class feature; this is because Paladins do not get Two-Weapon Fighting as an option in their class feature. This doesn't mean that Paladins can't do two-weapon fighting, but it does mean that they would need to take a level of Fighter or two levels of Ranger to get the Fighting Style feature, if it's important to them.
Notice as well that I didn't mention Barbarians in this section; Barbarians don't even get a Fighting Style option (at least none of the archetypes in the Player's Handbook do), so they do not have the option to take a Fighting Style without multi-classing, either.
Here's the next part of two-weapon fighting where people tend to do the rule wrong. Even experienced players can get this one wrong, as Cody of Taking20 does in his video essay on "Absolute Worst Dungeons and Dragons 5e Rules as Written". Cody wants to hate on the Two-Weapon Fighting rule because you can't use it with unarmed strikes. The rule could not be more explicit (on p.76 of the PBR, p. of the PH):
Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons).
Since the rule for Two-Weapon Fighting above only applies when you make an attack with a light melee weapon, you don't get to use it when making an unarmed strike, since an unarmed strike is not a weapon. In addition, since the rule specifies that you make the bonus action attack with a weapon that you are wielding in your other hand, and an unarmed strike is not a weapon, you cannot make an unarmed strike using the bonus action attack enabled by this rule. Cody may have a point when complaining that bar-brawler type characters can't take advantage of this rule, but he's completely wrong when he complains that monks can't use this rule. Well, he's not wrong that monks can't use this rule, but the point is that monks don't need to use this rule: monks in fact have two different class-specific ways to effectively dual-wield without making use of this rule, both of which are at least as effective if not more effective than this rule.
First, monks have access to the Martial Arts ability at level 1, which resembles the rule for two-weapon fighting quite a bit; a monk has to use a 'monk weapon' which is defined as a shortsword or a simple weapon that doesn't have either the heavy or two-handed properties. The monk can also explicitly use unarmed strikes, as per the text of the rule. When the monk uses the Attack action on his turn to make an attack with a monk weapon or an unarmed strike, the monk can then use a bonus action to make an additional unarmed strike. Though this ability is less restrictive in terms of what weapons can be used, it is more restrictive in that the monk is also restricted in his ability to wear armor or wield a shield. In addition, martial arts attacks start with low damage (d4), but improve as the monk goes up in level, eventually reaching a d10 in base damage. Lastly, unlike with Two-Weapon Fighting that prevents the adding of damage to the bonus attack without the enabler of a Fighting Style, the monk can always add his Dexterity modifier to damage with this attack. On the whole, I grade Martial Arts as at least comparable if not equal to 'base' Two-Weapon Fighting for classes that don't have access to the Two-Weapon Fighting Style.
But that's not all the monk gets! At level 2, the monk gains Ki powers, one of which is Flurry of Blows. The only obvious restriction on Flurry of Blows is that the monk must spend a ki point and a bonus action to make the extra attacks. But the benefits are that the monk gets to make two bonus unarmed strikes, the monk isn't required to be unarmored or not wielding a shield, and the monk technically doesn't even have to attack; the rule for Flurry of Blows only specifies that the monk "take the Attack action on your turn", not that they use it to make an attack or to attack with specific types of weapons. Thus the monk could use a Flurry of Blows after making a shove or grapple attack (PBR, p.77, PH, p.195). And the restriction of spending a ki point grows less onerous as the monk goes up in level, as the monk has a number of daily ki points equal to his level, and recovers them all after a long or short rest; in the correct party (a fighter, monk, and celestial warlock walk into a dungeon...), a monk can often use many times his normal amount of 'daily' ki points between long rests.
So the real answer to 'how do Monks use the Two-Weapon Fighting rule' is, they don't -- they have better options in their class features, so there's no real reason for them to ever need to use the generic Two-Weapon Fighting rule.
The Rogue is an interesting case for Two-Weapon Fighting. On one hand, most rogues find Two-Weapon Fighting a bit too restrictive for their tastes; not only does it require the rogue to close to melee range (where the lightly armored character tends to be less viable than the more heavily-armored and higher hit-die front-liners like the Fighter, Paladin, and the like), but it also requires the rogue to use her bonus action to make the bonus attack, which the rogue generally wants to use for other things, most commonly a Disengage via Cunning Action. Most significantly, the main benefit that a rogue would gain from making multiple attacks in a turn doesn't actually apply, since the bonus damage from their Sneak Attack class feature can only be used once per turn; while making multiple attacks does give the rogue more opportunities to make a Sneak Attack, and thus less of a chance to pass through a turn without using her Sneak Attack, the trade-offs for a typical rogue generally aren't worth it except in exceptional circumstances.
However, with the release of the Sword Coast Adventurers Guide came the Swashbuckler Rogue, a rogue archetype explicitly designed to try to make use of Two-Weapon Fighting. This rogue doesn't gain any additional 'uses' of Sneak Attack, but she does gain an additional condition in which her Sneak Attack applies (via the Rakish Audacity feature), as well as the ability to move away from targets she hits in melee combat without requiring she use the Disengage action (via the Fancy Footwork feature); the former allows the Swashbuckler more flexibility in attempting to land a Sneak Attack and the latter allows the Swashbuckler a chance to get away from an opponent she's struck with Sneak Attack without suffering that opponent's melee wrath. The Swashbuckler was re-printed in Xanathar's Guide to Everything, so Organized Play games presume you are using that version of the class, but there doesn't seem to be any actual difference in the two versions printed in SCAG and XGtE, so from a practical standpoint, if you have either book, you have the ability to play a Swashbuckler, which would appear to be the 'official' way to play a rogue who wants to make use of Two-Weapon Fighting.
If non-Swashbuckler Rogues have a difficult time using the Two-Weapon Fighting rules effectively, then the casting classes, for the most part, have at least as difficult a time using that rule. Generally, the reasons for this boil down to one or more of the following:
Casters generally use spells rather than weapons to deal damage, which can't be used to enable a bonus attack via Two-Weapon Fighting.
In most cases where a caster does make a weapon attack, they do so via the Cast a Spell action rather than the Attack action, which also prevents the attack from enabling a bonus action attack via Two-Weapon Fighting.
Caster classes that do allow for actual weapon attacks often have restrictions within their class that make Two-Weapon Fighting difficult if not impossible to combine with their key class features.
Most caster classes simply don't have spells to buff their existing weapons; instead they typically create weapons that attack on their own using the character's actions or bonus actions
Reason One is pretty straightforward: most casters deal their consistent round-by-round damage via cantrips, whether that's the Warlock's Eldritch Blast, the Sorcerer/Wizard's Fire Bolt, or the Cleric's Sacred Flame. None of these are weapons, so they can't be used to enable additional weapon attacks via Two-Weapon Fighting.
However, the Sword Coast Adventurers Guide introduced a trio of 'weapon cantrips', cantrip spells that enable weapon attacks. These cantrips, Booming Blade, Green-Flame Blade, and Sword Burst, allow a Sorcerer, Wizard, or Warlock (mainly the Bladesinger Wizard also introduced in that book) to make weapon attacks by casting a spell. Note, though, that the Two-Weapon Fighting rule specifies that the character use the Attack action to make a qualifying attack, and these cantrips don't make use of the attack action; they each use the Cast a Spell action, and specify that the weapon attack made during the spell is "part of the action used to cast this spell". Since these spells don't make use of the Attack action, they also do not enable Two-Weapon Fighting.
But a Bladesinger Wizard might decide they want to try Two-Weapon Fighting anyway; though Bladesingers in prior editions tended to use longswords, nothing in the 5e version of the Bladesinger requires the use of that weapon; indeed, a sidebar of Bladesinger Styles in the SCAG points out that hafted weapons like axes or hammers have their own style, and both the light hammer and hand-axe are valid weapons for use with the Two-Weapon Fighting rule. At this point, though, you run into a potential issue with the key class benefit of the Bladesinger, the Bladesong, which ends if "you use two hands to make an attack with a weapon". Though some DMs do rule that this only prevents a bladesinger from making an attack with a two-handed weapon or a versatile weapon wielded in two hands, DMs familiar with prior editions of the Bladesong will often interpret this rule as preventing the Bladesinger from attacking with weapons in two hands.
To avoid this problem, you can switch gears and instead make use of the Hexblade Warlock, a warlock archetype that explicitly gains a bonded weapon that they can use with their class features. So long as this weapon qualifies for Two-Weapon Fighting, a Hexblade can use that rule with their bonded weapon. And it's at this point that you encounter the final problem with using Two-Weapon Fighting as a caster -- Rogues can use the rule to try to more reliably land their Sneak Attack, and Fighters and Rangers have class features that make the rule more efficient when used as intended, but casters just simply don't have spells that can be used to take advantage of having a bonus action attack available via Two-Weapon Fighting.
There are spells that buff a character's weapon, but most of these spells are Paladin spells, such as the various Smite spells (Branding Smite, Staggering Smite, etc.), and though they are cast on you rather than explicitly on one of your weapons, meaning they would trigger from a hit with a bonus action Two-Weapon Fighting attack, they only trigger once, meaning that you're not so much getting more use out of the spell as ensuring that the spell goes off more quickly. Of the few spells that buff weapons that aren't Paladin spells, the main one in the Player's Handbook/Player's Basic Rules is Magic Weapon, which Organized Play and games based on its rules of awarding magic items has rendered all but irrelevant (when every character has a magic weapon by level 5, there's little reason to learn or prepare a spell whose only purpose is to make a weapon magical after that point), and as with the Smite spells, most of the other spells buff you rather than your weapon, such as Tenser's Transformation from Xanathar's Guide to Everything, or Tasha's Otherworldly Guise from Tasha's Cauldron of Everything.
Lastly, there are spells that summon or conjure weapons, but most of these do so to create weapons that act on their own. The most familiar to most players is the Cleric spell Spiritual Weapon, which not only doesn't qualify for Two-Weapon Fighting, but is basically what the Cleric uses instead of Two-Weapon Fighting, as both the casting of the spell and the use of the spell to attack while the spell is running make use of the caster's bonus action, and since the conjured weapon is superior to just about any off-hand weapon a Cleric might wield at low level, it's hard to see a Cleric choosing to make use of Two-Weapon Fighting when they could nearly as effectively just cast Spiritual Weapon. The spells Mordenkainen's Sword and Black Blade of Disaster do similar things, but at much higher level, and again basically have effects that make anything you might want to do with an off-hand weapon attack pretty much irrelevant.
About the only spell that would in fact enable a caster to perform Two-Weapon Fighting is the spell Shadow Blade from Xanathar's Guide to Everything (page 164). This spell creates a magical sword that counts as a light weapon and that you use with the Attack action, which would trigger a possible bonus action attack via Two-Weapon Fighting if you as the caster are actually wielding a second weapon that qualifies (or conversely, might allow this weapon to serve as the bonus action attack after attacking with a different qualifying weapon in your 'main hand'). The downside is that the spell is a concentration spell, which means you can't conjure a second one while you already have one, and the blade is defined as disappearing if you drop or throw it, which likely prevents another caster from conjuring one and giving it to you. The damage of the blade also scales up as you cast it with a higher level spell, meaning that classes with limited spell level caps like the Arcane Trickster, who you might think would be ideal for such a spell, wouldn't get quite as much value from it as the classes that get it directly on their spell list, the sorcerer and warlock.
So, without actually doing the math, it would appear that the best Two-Weapon Fighter caster class would be the Hexblade Warlock with the bonded weapon in the main hand, and a conjured Shadow Blade in their off-hand, triggered by the attack with their main bonded weapon. This also means that the Hexblade could still cast Shadow Blade without the need to take the War Caster feat (noted below) in order to 'set up' Two-Weapon Fighting mode.
Final caveats and thoughts
There is one last rule that can impact the use of Two-Weapon Fighting, and that is the Dual Wielder feat (PH, p.165). That feat grants a slight bonus to AC when holding a weapon in each hand, allows you to wield weapons that aren't light and still use the Two-Weapon Fighting rule*, and most significantly, allows you to draw or stow two weapons in the same amount of time that you would normally use to draw or stow one weapon. This last benefit exposes perhaps the biggest unwritten restriction of Two-Weapon Fighting: the 'free' draw or stow a weapon action that characters get each round only allows you to draw or stow one weapon. So if you go into a combat with no weapons drawn, in the opening round you cannot make use of Two-Weapon Fighting without this feat, barring something like the Fighter's Action Surge or a friendly casting of Haste before your turn: either you draw just one weapon, leaving you without a second weapon to use to make the bonus action attack, or you spend your Action to draw your second weapon ("Use an Object", PH, p.192), leaving you without an Action to use to even attack.
* - This brings us back to the quote that leads this essay: the author points out that, even with the restriction of only using light weapons removed via the Dual Wielder feat, you still can't use Two-Weapon Fighting with a weapon that has the Two-Handed property, as the rule requires you to make an attack with a weapon in one hand, which you cannot do with a weapon with the Two-Handed property. The trick is that the author notes that 'a lot of' weapons with the Heavy property also have the Two-Handed property, suggesting that there are some Heavy weapons that you can actually use in Two-Weapon Fighting. This is incorrect, as every weapon with the Heavy property on the weapons list in the PH and PBR (the Glaive, Greataxe, Greatsword, Halberd, Maul, Pike, Heavy Crossbow, and Longbow) also has the Two-Handed property. There are weapons with the Two-Handed property that do not have the Heavy property (the Shortbow and Light Crossbow), but these are both ranged weapons and wouldn't qualify for Two-Weapon Fighting even if the Two-Handed property could be removed.
A caster who wants to make use of Two-Weapon Fighting should also consider the War Caster feat, as that feat explicitly allows the casting of spells with somatic components while holding weapons in each hand, which without the feat would not be allowed.