When someone buys a firearm online, it must be shipped to a licensed dealer at the local level. If a handgun is purchased, it must be shipped to a dealer in the same state as the buyer, because handguns cannot be sold over state lines.
The buyer must then go into the local store and fill out the paperwork required by the federal government. This paperwork is known as a Firearm Transaction Record, or a Form 4473. The dealer then calls the information in to the U.S. Bureau of Alcohol, Tobacco and Firearms, and the required background check is completed. If a “proceed” message is received from the ATF, the sale may proceed, and the dealer usually collects a small fee from the buyer for their time.
The same is true at gun shows. There is not a time when a licensed dealer sells a gun at a gun show without conducting the proper and required government background check. The dealer then is required to keep these forms indefinitely and to give access to ATF agents during an investigation which may involve the purchaser or the firearm.
That is how it works, period. A dealer can be prosecuted and lose his or her business if found to be in noncompliance with these simple rules. What the government is trying to do is make sales between private citizens subject to a background check.