There are 50 different States here in the U.S. and each one has it's own highly convoluted list of rules, regulations, laws, and rules of thumb.
That being said, generally one applies for a license, pays the license fee if the application is successful (many times more applications than licenses are available and a lottery is conducted), and makes arrangements with landowners to hunt on their land or they hunt on public land. There are also licenses for small game where there are daily limits and possession limits.
I have spoken with Albert Alberts about coming to South Africa to hunt. He has recently contracted for some wonderful concession areas that are loaded with gemsbock, the animal I most want to hunt. My grand idea was to find someone to stay with when I arrive with my tool kit, build a bow out in the brush, shoot it in over several days of scouting, then settle down to hunt gemsbock. He's very interested in filming the whole process of making the bow thru the end of a successful hunt. More than anything, I am interested in getting the horns home to make a bow from them!!!