You can now get a Veteran designation on your WA driver licenses or ID card. If you're only changing your Veterans status, you will get a replacement license with the Veteran status added for free. (If you're renewing your license or adding an endorsement you will need to pay the normal fees for that.)
Bring your DD Form 214 that shows "honorable" or "general under honorable conditions" status to a driver licensing office. If you don't have your DD Form 214 you can request your military service records online, by mail, or by fax (archives.gov).