For the licenses you have to get a tag for the species and get a general season and if lucky you can submit for a special permit and get a special additional season.
Deer--you get a tag and declare your method--archery, muzzleloader, modern firearm, multi-season (if you're lucky). Then you can hunt the corresponding general seasons for that method. Usually only get one tag a year. So you kind of pick between blacktail, mule and whitetail.
Elk--Like above, but in addition to method you pick which sided of the state--East or west. East is spike/true spike unless you get a permit for a bull. Competition is tough for those permits. West is 3 pt or larger. West has good permits too, but not quite as competitive as east.
Bear and cougar, you buy the tag and get to use any of the methods.
There are also OIL (once in a lifetime) animals that are permit animals: moose, bighorn, mountain goat.
You can get tags online or at a retailer any time, but permits (and raffles) have deadlines for submitting.