Of course, one way is to drive until some campground sign appears on the roadside. After all, there are so many campgrounds in the USA that it’s hard to drive more than 50 miles without seeing one. In the beginning, we did that too, but after too many disappointments we do it differently now, even if we don’t know exactly where to stay the next night.
Our main tool is Allstays.com which comes as an app for mobile devices (it costs something), but you can use their website for a free search as well. There is a pro version available for a one-time fee that is much better than the free web search. Allstays has over 29,000 campgrounds and RV-parks in their database, with lots of information for each place, like phone number, address, category (private, national or state park, Army Corps, BML etc.). Pretty cool is a link to a web search for reviews about this particular campground.
Speaking of reviews: We almost never go to a campground anymore without having read at least a few reviews. We like best RVParkReviews.com, a website where reviews written by actual visitors are presented.