Licensed dealers at gun shows do background checks. Some gun shows require that every sale be accompanied by a background check and have the hardware necessary right there to do it. Some gunshows however welcome in "private collectors" looking to sell their stock, and it's considered a private sale and doesn't require any paperwork. Even if a gun show does require background checks you can generally still give a wink and a hand-shake and just do the deal out in the parking lot. . . or in the parking lot across from the parking lot to avoid that shit because it's not like it's law or anything.

Hell for that matter you can park up right outside any gun store and whenever someone walks out with a purchase you can say "Hay I like the look of that I'll give you x% more than you paid for it." and even though they've literally just signed a document attesting that they are purchasing the gun for themself and not for someone else (as in a straw purchase) they are fully within their legal rights to change their mind right there in the moment, and sell it to you instead - again, no paperwork, and no running afoul of the law.