While process servers in Washington state aren’t licensed, you will be required to register with the county auditor. Registration is $10 a year and there are no educational or testing requirements.
For your convenience, here are direct links to the five most populous counties (if your county isn’t listed, a quick Google search will turn it up):
For the most up-to-date version of the Rules of Civil Procedure, see the Washington Courts website.
Another helpful resource is the Washington State Process Servers Association.