OK
this will get you started, watch the next episode too which is on the state park just to the south west of the NP.
You can 'primitive camp' in the NP too, but you have to drive on gravel roads to do it. There is one long road, River Road, along the Rio Grande that has camping all along it and on other backroads, and there are many, you'll find marked camping spots. River Road is certainly worth driving, lots of interesting spots along it.
The park itself is huge and one of the least visited major parks in the system. The video above discusses the camping areas in the park.
I suggest stocking up before getting down there, prices are high no surprise. There is one mini-super market in Study Butte. There are a couple of gas stations inside the park. The busy time in the park is the cool season, the place is semi closed down in the summer.
There are many threads here about the park, you migh want to try a search.