Most bonuses come from a particular source; these modifiers will have an adjective to describe them, such as feat bonuses or class bonuses or circumstance bonuses or racial bonuses. Bonuses are always positive; if an effect would cause a bonus to be negative, treat it as zero instead.
If several bonuses apply to the roll you are about to make that all have the same adjective, only the highest one applies, and only once. For example, if you have a +2 class bonus to saving throws, and a +5 class bonus to saving throws vs. charm effects, then you apply the +5 modifier when making a saving throw vs. a charm effect, not the +7 that you would get from adding them together. However, if you have two different bonuses, such as a +5 class bonus and a +2 training bonus, you may add them both to the roll. Untyped bonuses are bonuses which have no type - you add all of these together when you make your roll.
Like bonuses, penalties often come from specific sources. If two or more named penalties with the same name would apply to your character, only apply the worst of those penalties. Unnamed penalties, on the other hand, accumulate without limit. Once you are ready to roll the dice, add all penalties that apply to the dice roll together and subtract that from the result.