While these are the most common uses for each of the die, different Dungeon Masters may require you to do speciailized rolls, or have their own rules regarding certain dice rolls. Not all rules are the same for every table.
The smallest of dice for the smallest of rolls. The D4 is mainly used for damage on smaller weapons such as daggers, or hit dice for tiny sized creatures.
It's also the most painful to step on.Most commonly used die for weapons. The D6 is used for small sized creatures, several class features, and the Sorcerer and Wizard hit die.
This dice is also used for rolled Ability Scores.The most "versatile" of the dice. The D8 is used for all weapons that have the versatility property, as well as the majority of the class' hit die and the hit die for medium sized creatures.
It's also commonly used for spells with healing effects and damage rolls.D&D uses two ten-sided die for a number of rolls. The D10 has the numbers 1-10 on each side, while the D100 uses 00-90 counting by tens. The D10 is also used for the Fighter, Paladin, Ranger, and large sized creature hit die.
When you roll both die, you can roll any number between 1 and 100.The strongest of dice. The D12 is used for huge sized creatures, the Barbarian hit die, and for certain damage-heavy attacks.
It's also the least commonly used die besides the D100.The most Popular of the dice. The D20 is used for almost every roll, making it the most essential of the dice. Saving Throws, Skill Checks, Attack rolls, and Initiative use this die.
It's also used for Gargantuan sized creatures