I'm not from Washington state area, but I would think the process is the same in most states. Lands are usually divided into Public and Private lands.
Public: State and Federal lands are usually open to hunting by anyone with a license. Sometimes the state property is divided into wildlife management units or something like that (terminology). For example, I'm in Tennessee and they are referred to Wildlife Management Units (WMA's). In Pennsylvania, the open property is termed "State Game Lands". In the west, there are also BLM lands (Bureau of Land Management) which are federal land that is usually open to hunting. Military property is also sometimes open to hunting (with restrictions). Some states allow hunting on state park land. National parks are generally off limits to hunting.
More research in this area is needed prior to choosing an area to hunt. The state fish and game department should be able to help you in this regard. Go to their web site. Folks in stores and gun shops or sporting goods stores can also direct you generally as to ways to find accurate information. National forests are usually open to hunting without restrictions.
Private Land: Many of the timber companies own tremendous amounts of property. Their property is frequently open to hunting. Some sort of pass is usually required and there may be a fee. Lands owned by regular folks may be open to hunting, but permission is required. Sometimes private land is leased by a hunting club, and members only hunt on the property. They pay for the access right basically. You have to do the leg work. Talk to people and ask questions.
Nobody is going to tell you their exact "spot". But most will tell you that they hunt on such and such mountain or area near xyz (town). You can usually find these places on the internet. The USGS web site is useful for topographic maps (for free).
On private land, it is necessary to learn the limits of the property. Hunting a 25 ac property may be okay but a 5 ac property is too small. Get premission to hunt on private land. Knock on doors.
If there is no much public land, then look to the hunting clubs and try to join. You will then have access to their property. Price may range from $100 to several thousand per year.
To me, the most important thing is to just get started and do your research.
Once you have access to a property, go and start scouting the property for deer sign (I assume it is deer.) There are gobs of hunting articles and books written about deciding on a spot to hunt. Different animals, different approaches. At first, you may literally be just parking and hiking back and finding a place to stand that you can see. You should be looking for food sources, trails, rubs and scrapes (deer), water sources, etc.
The best way (and certainly the easiest approach) is to find someone you know who hunts and tag along with them on the property that they hunt to start and go with them on the scouting trips. During those trips, you will be discussing location, animals, tracks, trails, etc. It's fun. Whole books are written on the subject.
Anyway, good luck. It may not be as simple as looking on a map and saying "I'm going there." or near such and such town or mountain.