There's pretty much two big distinctions you need to think about when talking about back country camping.

National Parks are generally very limited as to where you can camp. Its basically always going to be in a designated campground, although they may have some backcountry campsites available.

National Forests and BLM lands are often much more open to camping "anywhere." There are usually some restrictions as to how far from a road or river you must be, and as always its pack in/pack out, and you're encouraged to use existing campsites rather than "bushwack" your own site if possible to reduce the amount of damage you do to the forest.

In these cases, you still need to check with a ranger station in each forest/area to see what the specific rules and restrictions are for any specific area in which you hope to camp.