Here's what you do, Maximus.
Find a local gun range in your area. Go down there and tell them you want them to teach you how to shoot. They'll probably make you buy the bullets there and possibly pay a gun rental fee, but you'll be able to shoot a few different guns in a few different calibers.
As far as "gun licenses" go, thanks to the 4th Amendment there really is no such thing. Laws vary a bit by state, but basically once you clear the background check and (maybe) have to wait for a "cooling off" period, the gun is yours. If you want to carry the weapon around with you, that's where it gets a little trickier. You have to apply for a Concealed Carry Weapons (CCW) permit, and this allows you (depending on your State) to legally carry a loaded weapon (or a knife longer than 3" or nunchuks, etc.) on your person. Again, laws vary depending on state.
But, you don't need this to legally own and shoot a handgun. And, you can keep the thing loaded in your house all you want (etc.) provided you don't try to carry it concealed outside without a permit. AND, even if you have a CCW permit, you can't "brandish" the weapon or risk being arrested. You are only allowed with a CCW to have it concealed on your person and pull it out if you are threatened with deadly force.
Long story short, probably best (as a complete newbie) to go to a good gun training course. Check a local gun range. I'm sure they'd be able to help you out. Most of those guys are, believe it or not, incredibly nice and helpful. Just don't get too wrapped up in it and do something like make an impulse purchase there. While nice, helpful people interested in teaching you about guns, they are definitely NOT generally known for being reputable and upstanding salesmen.
-copro