Some private campgrounds have a Request to Book button that allows you to request a reservation with the campground. More and more campgrounds are enabling booking requests through The Dyrt.
And brand new...very soon...some campgrounds will have instant bookings available!
With National Parks and State Parks, they all filter through the rec.gov reservation system, so those are straightforward systems with guaranteed reservations if you make them. With private campgrounds, it's different. Each one uses a different method, and some use third party sites outside of ours. Beyond that, there are others, still, that like the old fashioned method of a telephone call and take reservations on paper. There is no good way for us to incorporate all of those methods into one system.
It's best to contact each campground directly to find out the best and most up to date information about their own reservations.