Licensing requirements depend on what state or country you're in. Here in Florida, you don't need a license to purchase a firearm. You do, however, need a license if you're going to carry a concealed firearm.
That being said, even though there isn't a licensing requirement, there are still restrictions on buying firearms. If you were to walk into a gun store and purchase a gun, you'd have to fill out the ATF's form 4473 which includes questions about whether or not you're a felon or otherwise disqualified from gun ownership. The dealer also calls the NICS to run an instant background check on you to make sure you aren't lying when you claim not to be a felon. Finally, here in Florida, there's a waiting period if you don't have a concealed carry permit.
