Public Health - Seattle & King County recommends testing right away for anyone with symptoms consistent with COVID-19 or who has come in close contact with someone who has COVID-19. The availability of testing kits is increasing. Tests are generally administered through a primary healthcare provider but there are options for those who don't have healthcare access.
It's important to self-isolate while waiting for results even if no symptoms are showing, because COVID-19 can spread before symptoms appear. Those who test positive may receive a call from Public Health. The caller will ensure you have care and will ask about how you may been exposed to the virus, and who may have had close contact with you while you were contagious, so they can get tested and self-isolate as well.
Additional Resources
Public Health–Seattle & King County: COVID-19 testing
Public Health–Seattle & King County: Public Health's "Symptoms, testing and care" resources
Washington State Department of Health: Testing for COVID-19