Whenever a player character attempts an action that has a chance of failure, roll a twenty-sided die (d20) and add any relevant modifiers. Compare this number to the target number (DC, or "Difficulty Class") the GM has set for the task. If the number matches or exceeds the target number, the task is successful.
The game uses the same set of polyhedral dice as the D20 System it is built off of. Each player should have a set of dice that include a d20, d12, d10, d8, d6, and d4, as well as percentile dice (d100). It is advised to have multiples of each dice, as many actions in the game require rolling more than one of the same type of dice (written as a number before the dice type. For example, rolling 3 6-sided dice would be written as 3d6).
A modifier is any number that gives a bonus or a penalty to a roll. Bonuses add to a roll, penalties subtract from a roll. Modifiers normally stack with each other unless the modifier comes from the same source (for example, two casts of the same buff spell), in which case the higher number (or lower number if it's a negative effect) applies.
The bonus or penalty associated with a particular Ability score. An ability modifier (not the ability score) is used whenever an Ability Check is called for.
The bonus applied to a character's AC from their equiped armor.
The bonus or penalty from the use of Alchemical Items such as potions or poisons. These are almost always temporary bonuses or penalties.
A bonus stemming from the character's background.
A bonus stemming from the character's birthsign.
A circumstance bonus or penalty is a temporary modifier given due to specific, circumstantial conditions that affect the outcome of the current task. A circumstance bonus is temporary and only applies when the condition that caused it is still present.
An enchantment bonus is the benefit granted to the user by a specific piece of enchanted equipment. The bonus applies as long as the item is worn and the character has the ability to benefit from the enchantment. If a character has already exceeded their maximum number of enchanted items, any additional items can be worn but only function as their non-enchanted equivalent and the enchantment bonus cannot be applied.
A character's race determines a small number of bonuses or penalties to various things such as ability scores, starting skill levels, damage resistances, etc.
A resistance bonus applies to a particular Damage Resistance. Resistance bonuses stack as long as the source of each bonus is different.
A trait bonus is any bonus that is granted by a specific character Trait.
In some circumstances (such as from a spell, a character ability, potion, etc), a character may be given either Advantage or Disadvantage on a roll. When this happens, roll 2d20s instead of one, and use the higher number (if granted Advantage) or the lower number (if granted disadvantge)
If your gaming group prefers exact modifiers to advantage/disadvantage, treat advantage as a +5 modifier and disadvantage as a -5 penalty instead of rolling two dice.