These are some ways to RV:
- Parking Lot One-Nighters - driving late and just want a place to sleep such as the popular WalMarts, Cracker Barrels, Cabelas, truck stops, rest areas, casinos, fairgrounds
- Boondocking - normally done on national forest or BLM lands. There are regulations so you'd have to check with each agency. You most likely would be driving a gravel road, finding a suitable spot for the RV - many times around no one else, and spend some days there. You'd drive your vehicle around to sitesee, go fishing, etc.
- Dry Camping - using a designated campground with camp sites. There 'could' be a dump station and potable water fill area for your tanks but there would not be hookups. You could find these sites in national forests, Corp of Engineers parks, national parks, state parks, county and city parks. Even some BLM lands have designated campgrounds without hookups.
- Private RV Parks - can have a mix of hookups or all full hookups
RE: your question about national parks - there is a big mix of type of sites within the parks. Very seldom will you find full hookups except Yellowstone and Grand Teton do have a concessionier-run park with them.
Some will have electric such as in Zion. Most will not have hookups but will have a dump station and a water fill area. Usually there are water spigots throughout the campgrounds but they are not intended to be used to fill up your RV tank. They are for filling a bucket or water jug to take back to the campsite.
Whenever you go to a national park, definitely check their web site for lots of good information including campground, roads, things to do, etc.