Asking you as someone who knows a lot about Stupid Dice Tricks - what's the simplest way to get a one-tailed distribution using conventional dice? (i.e. numbers from, say, 1 to 5-ish are fairly common, but there's a small-but-nontrivial chance of ending up with results up in the 20s and 30s)
"Simplest" is subjective, but the most conventional way of doing that involves "exploding dice", a dice-rolling method in which each die is read as its face value for any non-maximal result, but when rolling the maximum possible value, another die (typically of the same size) is rolled and added to the initial result. For example, an exploding d6 might roll a 6, then a 6, then a 3, for a total result of 15 on 1d6.
While straightforward, this method has the issue that certain results are impossible; for example, you can never roll exactly 6 on an exploding standard d6, since the minimum result of the additional roll is 1. This has historically been addressed in several ways:
Rolling with a base of zero rather than one. This is most commonly done with d10s, since a standard d10 is already numbered 0 through 9, though it can also be achieved with other die sizes either using non-standard dice (e.g., a d6 with faces numbered 0 through 5 rather than 1 through 6), or by reading a standard die in such a way as to produce equivalent results (e.g., reading the 6 on an exploding d6 as 0, with the exploding result occurring on a 5). This approach avoids unrollable values, but has the drawback that the extra roll sometimes does nothing, which can feel anticlimactic.
Treating the value of the exploding result as equal to that of the highest possible non-exploding result; under this method, rolling a 6 on an exploding d6 would be treated as "5 + reroll" rather than "6 + reroll". This avoids both unrollable values and rerolls that do nothing, but in my experience, a lot of players just can't get their heads around it, and will always forget to read that 6 as a 5, no matter how many times they're reminded.
This technique can also be adapted to "hit-counting" dice pools; for example, rolling a number of d6s, counting each die which rolls 4+ as one "hit", and additionally rolling an extra die for each die which rolls a 6. This is broadly equivalent to variation 1, above, and suffers from similar drawbacks.
Apart from exploding dice, other reasonably popular approaches include various "dice poker" methods, in which a number of (typically identical) dice are rolled, with the result ordinarily being read as the highest single value, except that certain combinations of numbers are assigned special values. One of the simplest variants involves the summing of doubles, triples, etc.. For example, rolling 3d6 and getting results of 2, 4 and 5 would be read as 5, but a result of 2, 5, and 5 would be read as 10; however, a result of 2, 2, and 5 would still read as 5, since the sum of the double is lower than the highest single. Alternatively, the dice can be read so that all doubles beat all singles, all triples beat all doubles, etc., for a more truly poker-like distribution of results, though this can make assigning target numbers tricky.
A notable twist on the above is the "place-value" dice roll, in which the die's face value is read as the "ones" place, and the number of dice showing that value as the "tens" place. This is typically done with d10s to keep the place values intuitive; for example, rolling 5d10 and getting results of 2, 3, 3, 7 and 9 would be read as a result of 23. Hybridised with hit-counting dice pools, the place-value method becomes the One Roll Engine's "width x height" method of reading the dice, which is definitely worth checking out if you want to delve deeper into this topic.
(An important distinction between exploding dice and dice poker/place-value methods in the particular context of dice pools of variable size is that it's always possible, if increasingly unlikely, to make a roll where nothing explodes, but beyond a certain point, "exceptional" results on a dice poker/place-value roll become inevitable. For example, with a pool of 7d6 it's impossible not to roll at least doubles!)