TexasCHLforum.com

I can't speak for other states, but let's pretend the site is Texas based. This is simply a listing site. If you find something on this site you like and want to buy it or if you have something listed someone wants to buy, one contacts the other and makes arrangements to meet. You can then conduct a face to face transaction.
Assuming you have no knowledge that a person is not eligible to possess a firearm and you are both residents of the state (we are pretending the site is in Texas), you can sell a firearm to that person or buy a firearm from that person without a background check.
This must be face to face. If not, the firearm would have to be shipped to a FFL and a background check done.

Obviously some states have laws that would complicate the above transaction.