RE: How to draw tags?
I think that the first time you go out for something new whether it be a new species of fish or big game, it is helpful to go with a guide or at least someone very knowledeable on that particular species. Yes, you can get scewed there too, but for the most part you don't. There are some areas and species you can hunt public land for with OTC tags, but I don't know what you are going after so I can't tell you for sure that what you want to hunt is that way. Like TX said, a call to the state's DOW can be a huge help. They will tell you what areas have the highest #'s of species of game, highest success rates, etc. They will also help you find access to those areas, etc. They may also know respectable guides around the area. It is definitely worth a call to them.
Applying for a tag is pretty easy. Most of them are online these days. Only problem is you generally have to pay up front and if you DO NOT get drawn you get your $ back. Kind of stinks, but you have to do that some places even if you are only putting in for preference points and there is a 100% probability that you will not be drawn for a tag.