I'm sure the policies vary from one place to another. Best thing to do is call to inquire about space, prices, etc. And some of them will be listed in uscampgrounds.info--a great place for info on all publicly-owned campsites.
When I stayed at the Faribault County fairgrounds, in Blue Earth, MN, there was no one else there camping and we never saw any fairgrounds personnel. There was a sign posted with the rules, and a box for donations. The site was free for up to 3 days, with full hookups. (We did leave a donation.) It was on a gravel lot with 4 other sites. Not scenic, but quiet, & fine for an overnight.