Activated a trap when I wasn't able to do so; how is this handled?
If I played a trap card that I was not allowed to play, do I destroy it or put it back down?


Well, this will depend on the nature of the game you are playing:


If this was an official game/tournament: In this case it will be up to the Judge to determine the course of action to follow. It could be from a simple replay (rewind the actions made), or up to a penalty or game loss.
If this was a fun/friendly game, not official: Then it is up to you and your opponent to decide what to do. If you are able to replay or rewind moves go for it, otherwise discuss what should be done.


... Still, I suggest you be careful in either case, as you are not only revealing your cards to your opponent, but you could end up with a penalty or game loss in a tournament.