Factual Mistake in the previous "Factual Mistake". In most states a private individual can sell a firearm to another private individual in a face-to-face sale without conducting any sort of background check. This is often referred to by the ignorant media as the "gun show loophole". Which has nothing to do with gun shows.
A person cannot buy a handgun in any state without a Federal Firearms Licensee running a Federal background check. Also no one can buy a gun that does not live in the state of purchase without sending the purchased weapon to a FFL in the state of residence, from the FFL that the weapon is purchased from, and obtaining a background check for EACH weapon Being purchased.