If I bring an iPhone I bought off Craigslist to AT&T, what happens?

Is there a fee I have to pay? Do I have to sign a contract or can I just pay the bill for it, since I don't have to pay it off.

You will be fined if you do that.

Q: If I bring an iPhone I bought off Craigslist to AT&T, what happens?
A: Nothing "happens". It all depends upon what you ask of them when you show up.

If you bring them a used phone to put service in, it doesn't cost you anything and you don't have to sign a contract. You just pay what your bill regularly is and that's that.