It's just like buying off EBay. Buy the gun, pay for it, and then send the seller your local gun shop address and FFL (tell them first that you're going to be transferring a firearm through them), and it'll show up in a few days. They'll run your background check there and that's it. You'll probably incur a $30 transfer fee as well.
Generally speaking holes in anti-gun theories are called "facts."