Despite what the media would have you believe, guns in the USA do have restrictions. :-) Pretty complex ones too (and the reasons as to WHY the various restrictions exist are even more complex). I'll just do a quick rundown on the basics, since whole books can be written about this stuff.
In USA: 18 years old to buy a longgun (rifle, shotgun, etc), 21 years old to buy a handgun. interestingly, Uzis can be configured either as a "handgun" or a "longgun" depending on barrel length and stock. True automatic weapons (multiple rounds fired per trigger pull) are VERY tightly controlled under the NFA act (1968 I believe?) as are armor piercing bullets, but letting others use it while the NFA responsible party is present is legal. Kids are allowed to shoot, but there must be a responsible (in theory, apparently some are not terribly responsible in practice) party of age with them. NICS federal firearm background check must be performed on all transactions that involve a Federal Firearms License (not all do, and those that don't require the seller to not sell to convicted felons, etc).
From there on it varies widely state to state. Where I live (Ohio), no gun permits required and it's legal to openly carry guns where not otherwise restricted (there are a ton of restricted zones, including 1000 foot school safety zones that make it pretty much impossible to legally do in any town or city). Concealed carry only permits handguns (no longguns, no knives, not even a taser) and requires training, another background check, and registration with law enforcement. It also is subject to a set of restricted zones (different from open carry). Any gun that holds more than 33 rounds (except for .22lr caliber) is defined as an "automatic weapon" (even when it's not automatic) and then falls under the MUCH tighter restrictions. Sound suppression devices are also very tightly regulated.
Oh, and we seem to be the most litigious society around. Make an error in firearms judgment and you may not go to jail, but you might as well since you'll end up penniless and living under a bridge in a cardboard box. :-)
That's the super short summary. :-)