Characters have a proficiency bonus determined by level. Monsters also have this bonus, which is incorporated in their stat blocks. The bonus is used in the rules on ability checks, saving throws, and attack rolls.
Your proficiency bonus can't be added to a single die roll or other number more than once. For example, if two different rules say you can add your proficiency bonus to a Wisdom saving throw, you nevertheless add the bonus only once when you make the save.
Occasionally, your proficiency bonus might be multiplied or divided (doubled or halved, for example) before you apply it. For example, the rogue's Expertise feature doubles the proficiency bonus for certain ability checks. If a circumstance suggests that your proficiency bonus applies more than once to the same roll, you still add it only once and multiply or divide it only once.
By the same token, if a feature or effect allows you to multiply your proficiency bonus when making an ability check that wouldn't normally benefit from your proficiency bonus, you still don't add the bonus to the check. For that check your proficiency bonus is 0, given the fact that multiplying 0 by any number is still 0. For instance, if you lack proficiency in the History skill, you gain no benefit from a feature that lets you double your proficiency bonus when you make Intelligence (History) checks.
In general, you don't multiply your proficiency bonus for attack rolls or saving throws. If a feature or effect allows you to do so, these same rules apply.