Just buy one, but bring plenty of cash!
As far as I know, you just buy one from any of the regular sellers (sporting goods stores, Walmart, Some hardware stores, etc, the sell them a lot of places.
However, bring money. I looked through a 2009 hunting guide. If you are from out of state, get some good maps too, cause they have lots of special game managment area and seasons.
Couldn't find anything in the booklet about non-resident licenses, except, non-residents have to buy them, and the fee schedule.
Holy Crap!!!
The non-resident license costs 10 times what the resident's does. So, if I pay $75 for license and game tags (and you need those too!) non-resident pays $750!
Hunting is good, but season rules and areas are complicated, and it ain't cheap, at least not in my income bracket,
If you got the time, and the money, come on out. They really only hate hunting in metro Seattle, but then, those people hate a number of things. Unfortunately, they have a hand in setting the fees!