Okay, I took advice from a guy who really DOES know a lot about gun sales ----- in Maryland.
First off, there are big differences in state rules.
In Maryland, there is of course a waiting period for buying guns from gun shops.
At gun shows, there is no waiting period for most guns. They do give you a 20-question form to fill out -- Are you crazy? Do you beat your wife? Like that. Really. From his description, I am dying to see one of these forms. And then they call in your name and social security to a central clearing house that quickly clears the transaction in seconds, and then you carry off your gun. Obviously they clear pretty much everyone, even if they are certifiably crazy. The craziness records are not getting thru the system, as we all know by now. The system is very quick: it is designed to sell guns, not to stop the sale of guns.
HOWEVER, there is a category of guns that you have to wait on even if you buy them at the shows. In Maryland that is all hand guns AND all assault rifles. You fill out the form, you pay, you either drive a week later across the state or they will send it to a licensed gun dealer near you, for a small service fee, like $10. In Ohio, there is NOT a waiting period for the handguns, at least, as we heard from a friend who bought one and walked out with it. Actually, I once bought a handgun in Maryland and walked out with it from a shop, but that was before the Brady Bill passed, I believe, years ago.
Another option at gun shows is the private sales, that are completely exempt from the forms and phone check: this works by men carring a rifle or whatever around the show with a sign held up saying what it is and the price, and private sales are allowed by the show (surprised me: selling animals privately on the grounds is definitely not allowed at livestock auctions, but they do allow private sales at Maryland gun shows, very colorful).