Most places in the United States do not require you to register a bicycle. In certain towns, that do require registration, it's a matter of going to the local municipality and providing the serial number that is located on the underside of the crank.
It's a good idea to copy this number and save it in a safe place. If your bike is stolen, you can report it to the local police department, pawn shops, etc. Some people have recovered their stolen bikes by posting a picture and a stolen comment on Craig's list. Other Craig's list buyers will sometimes notify the poster of a for sale listing of their bike on the list.
Best thing to do is buy a really good lock and keep it locked up.