If you do not go through and FFL (Federal Firearms Dealer) dealer with export license (as Spooksar correctly noted) then you have a much more confusing path.
Here in the states, each state (rather than the Federal Govt) controls the sale of firearms, to some degree. A licensed FFL must abide by Federal guidelines, but there are other options. If you have been resident for 90 days (as a student or working on a visa) you are eligible to purchase. If you go to a private party sale (individual to individual) these can be even less restrictive. Again, the state is all important. In some states such as Illinois (home of Chicago) you must have an FOID (Firearm Owner ID) in order to possess or purchase arms or ammunition. In other states such as KY you simply need a clean criminal record. In my case, being retired military, I have walked in, chosen a firearm, completed the purchase, and walked out in 30 minutes or less. After purchase, no record is kept, so I can then dispose of the firearm as I see fit.
Interestingly, it is the states and areas with the most restrictive laws that also have the greatest incidence of firearm crime. Seems the criminals aren't too keen on obeying the laws - imagine that