A: If a Creeper is drawn by the active player, they must take the Creeper (play it in front of themselves) and draw to replace, such that all the cards they have drawn for whatever the Action indicates will contain no Creepers.
For example, if I play Everybody Gets One, then I, as the active player, am the one drawing cards. As such, I have to take all the Creepers I draw, redrawing until I’m holding enough non-Creeper cards to give 1 to each player including myself. In a deck with a lot of Creepers, anything that makes you draw cards is a liability!
There are a few cases where a card instructs you to discard Creepers encountered, in which case you do that, but the default is that the active player must accept them until the appropriate number of non-Creepers has been drawn.
There are also a few cases where it’s not necessarily clear, and we have FAQs that give rulings on those:
Q: What happens if a Creeper comes up when Pandora’s Box is played?