Go to the local Spokane County Sheriff's Office in the Valley and apply. Take your ID permit. I got mine through Whitman County via the Pullman PD (I go to U of I). I walked in told the nice lady behind the counter what I was doing and she was very helpful. I filled out the permit info, got printed paid the fee and went home. It took maybe 10 minutes.
About a week later I had my WA permit mailed to my parent's house in Boise. and I picked it up during my Fall Break. I did laminate it at the recommendation of the PD officers in Pullman. The ink will come off very fast otherwise. It is not like the ID permits and doesn't fit with your DL. Mine sits behind my electronic work key card.
It was a painless process for me.
To OC you DO NOT need a CPL. I used to OC in Pullman and Spokanistan before I had my WA CPL.