>>315863/k/ here. It varies state by state, but in all of the states I've lived in, all one needs is a valid state drivers license or state ID, and to obtain one of those, all you need is a piece of mail addressed to an in-state residence.
In some states, there are restrictions on non-citizens, but as far as I am aware, even these restrictions are cancelled out if you obtain a hunting license.
More generally, to buy a gun, one must pass a background check (have you ever been arrested for domestic battery or a felony? Are there open arrest warrants in your name?) that is conducted by an FBI data system, pay a small processing fee. The background check generally takes anywhere from 10-30 minutes. To obtain a hunting license (these are issued by state governments) you generally just pay a 20-50usd fee.
