Wyoming is an awesome place to hunt on a general tag. General tag allows you to hunt 90+% of the state. Deer, bear, wolf and Elk are general (over the counter) tags. Each area on the hunting map has defined borders and the season dates can vary from one area to the next. If you want to hunt a specific area, such as a special park permit for the national park north of Jackson, you need to put in for that specific area. If you don't draw that tag you can still buy a general tag. General elk, in most areas for most of the season, means you can shoot any elk. Different areas have dates that go from any elk to bull only or cow only.
Any license not issued in the draw goes on sale at half price later (often times there are out of state cow/calf elk leftovers too that can be purchased over the counter). You can buy your general elk tag and then purchase a half price cow/calf tag when they go on sale (2 elk is nice). Antelope, bighorn sheep, buffalo and moose are all special draw tags. If you draw a moose tag you can't put in for moose for 5 years. Moose and bighorns are on a point system. Buffalo is random every year. Wyoming draws based on the point system for some animals but they put in 25% of that specie's tags into the general draw (4 moose tags in an area 3 are issued based on points and 1 is drawn from everyone regardless of points).
One notable difference from most states is the hunter has to carry his/her hunter safety card in the field. You must reside here for one full year before you can purchase in state tags, and if you hunt in another state this year as a resident it postpones that for one additional year (I think). If you don't fill your tags here you were too lazy to get out and hunt or you held out for a ginormous one and didn't find it. Big game hunting here is awesome!