Easily the most complimented feature of my writing has always been how strongly I convey emotion, so here's my unsolicited advice on making your readers feel what your characters are feeling:
Physicalize - I am personally a very emotional human being, and I feel things very physically. I think that helps me describe emotions on paper, because I tend to connect emotions with physical sensations. For example, instead of "he felt sad," I would say "sadness washed over him in a lukewarm tide." That physicalization of the abstract feeling can make it easier for people to replicate the feeling in their own minds. So basically, I'm taking the emotions I want to convey and thinking, "how does this emotion feel on a physical level?" and then describing that. "Anxiety tightened in her gut." "Anger bubbled under his skin." "Her body was light, drifting in euphoria." Metaphors are your friends.
~Body Language~ - Another physical indicator of emotion is how people's body language changes to reflect what they feel. This is huge when dealing with non-POV characters. Any time that you could say "she looked upset," you would do better to just describe how she looked. "She furrowed her brow, looking down." "His fist tightened on the door handle." "The silverware rattled in the drawer as she jerked it open." Emotions often come through in the way characters interact with objects around them. In that vein, you can usually express it more clearly if you focus around some action that the character is performing (even a tiny little one). Making note of details like avoiding eye contact, how/when people fidget, whether their movements are sharp or fluid, and stuff like that can go a long way in conveying emotions more naturally.
Wait How Do People Talk Again?? - Dialogue can be really tough if it doesn't come naturally to you. I voice-act quietly to myself pretty much all of the dialogue I write just to make sure it sounds natural. Again, pulling from real-life experience is usually best here; imagine how you've heard real people talk when they are feeling angry, depressed, panicked, etc. Think about phrasing and tone inflection - do their words sound short, sharp, and clipped? How do their phrasing choices show that? Do they ramble in a bright, bubbly tone? Are they monotone and flat? Do they use a lot of filler words because their brain is moving too fast (or too slow)? Are they so tired or hesitant that they trail off or pause frequently?
That's my main advice on conveying emotion through writing. Feel free to add on or ask questions!
