Participating Washington community colleges, colleges and universities will waive all or part of your tuition and fees for up to 200 quarter credits or the semester equivalent. The state also provides up to $500 a year toward textbooks and course materials. Each school runs its own waiver program, so how much is waived depends on where you enroll.
Contact the admissions or veterans office at the Washington school you plan to attend and ask about their tuition waiver for veterans. The waiver is granted by the institution, not by the state, so nothing is filed centrally.
Your DD214 showing an honorable discharge and qualifying service, proof of Washington residency, and whatever enrollment paperwork your school asks for.