We just spent two weeks in Big Bend and hope to have it up on the blog in a few days. I recommend a little book called "The Big Bend Guide" by Allan Kimball. They sell it on Amazon as well as at the park. John didn't like the organization but we referred to it repeatedly. It covers the Big Bend area, not just the national park. As for the park, we booked a site in Rio Grande Village for three nights. Once there, you can walk around the non-reservable sites and look at the tags for dates people are leaving. We then "played vulture" and waited until the campers came home, asked nicely if they were leaving the next day or extending (leaving), then stuck our tag under theirs and claimed the site. The "campground full" signs go up before the campground is full. Check the camp host board for the Rio Grande campground and you may get one night in a reservable site that wasn't booked online which puts you in place to claim a non-reservable site after that. Rio Grande probably had a dozen or more sites open up each day but there were a lot of people vying for them. ALL campgrounds were full by 10 or 12 when we were there.
NPS has three campgrounds, all no hook up. Rio Grande Village/east side (any size rig, generator area allows use 8-8, dump station nearby), Cottonwood (any size, NO generators, NO dump station), Chisos (road recommendation rigs no longer than 24 feet). There are also backcountry sites that a Phoenix could get into (and many I wouldn't take the road into) but no generators allowed for those and not sure where they dump, maybe down at Rio Grande. We couldn't take the rig up to Chisos so camped 9 nights at Rio Grande and toured the east side and Chisos then moved (really early) to Cottonwood and toured the West side.
If you want hook ups, you have to book the concessionaire campground also at Rio Grande Village. Our new solar suitcase kept our batteries charged and we dumped at Rio Grande each time we switched sites.
If you like to learn, do the ranger programs! PM me if you have questions. I might be able to answer them.