All of the Park is designated camping only. Some sites, not 53, must be reserved. Those are usually ones that permit horses too. If you don't stay at a reserved site, all you need to do is go by a Ranger Station and register. There's one at each side of 441 at the Visitor's Center. Be sure to check what sites are closed for bear activity. All sites also have cables for hoisting up your food and other smelly stuff. Use them.
With the cables, the mice are more of a problem than bears. I've heard there is a good food bag out that has some sort of re-enforcement in it they can't chew through. You might check out your local outfitter for one of those before you go. They love peanut butter bagles and any kind of gorp.