There's no such thing as the "gun show loophole". It's a myth. There already are background checks. I can tell you've never even tried to own a gun.
Now, what you can also do legally in most states is purchase a firearm from another private individual through a private sale. An enormous number of second-hand gun sales occur in this fashion, through Craigslist or classified ads or personal acquaintances. Effectively, this is no different than if you were buying and selling lawnmowers or comic books, or any other mundane object. I am skeptical of any attempts to really regulate this activity, because it is effectively unenforceable given the number of firearms currently in circulation and the almost complete lack of any records of ownership history for most of them.