Turkeys are my favorite game to hunt in North America, at least out of the species I have hunted thus far. There is nothing like the thrill of a turkey gobbling on a crisp spring morning, then calling it in. I'm very much a "run and gun" type of turkey hunter, which while it may see less success, is very much more exciting.
To hunt turkeys you will need a hunting license. Before you can purchase a hunting license, you must take a hunter safety course. In the spring season (when they gobble), you are only allowed to harvest males. It is absolutely amazing how tough turkey hunting is!
The legal implements for turkey hunting are shotgun or bow. Rifles are not allowed, except perhaps in 1 or 2 states. There is a real art to turkey calling, which takes a tremendous amount of practice. There are also many different types of turkey calls. I personally use a box call and a slate call.
Any particular questions regarding turkey hunting, feel free to PM me. A side trivia note - there are four subspecies of turkeys in North America, and turkeys live in 49 out of the 50 states (all except Alaska). There are also the Gould's turkey (primarily in Mexico) and the Oscellated turkey in South America. Harvesting all four subspecies of North American turkeys is called a Grand Slam.