[1ViciousGSX]

If a business is selling guns at a gun show, the laws are already there and in place.

http://smartgunlaws.org/background-checks-in-louisiana/
From the Louisiana page, but federal law extends to all states:
"Federal law requires federally licensed firearms dealers (but not private sellers) to initiate a background check on the purchaser prior to sale of a firearm. Federal law provides states with the option of serving as a state “point of contact” and conducting their own background checks using state, as well as federal, records and databases, or having the checks performed by the FBI using only the federal National Instant Criminal Background Check System (“NICS”) database."

Now I would hope all dealers at a gun show are registered dealers and not just Billy Bob "Big Gun" Johnson selling his used .38 special.

Private sales are just that, private sales that can't be tracked other than a bill of sale. So that is a bit tougher.