How does Steam find and ban hackers?

Awesome! One more reason to love Steam.

Probably log IP's. So the person who hacked your account probably already had one of his own, and since the IP's matched, Steam was able to ban his other account.

Simple really.

The thing with Steam is the constant net connection, they send out a PING every few seconds that checks on the IP and for "hidden" files and folders that are installed on your PC after setup, now as for how they catch them IDK, but I do have a hacked account on STEAM and I used it to play all my games which I never payed for so there are upside to haveing a good hacked accound and then having your account hacked!

^^ You don't need to be connected to the net; they DO have an offline mode...