Washington contracts with PSI Exams which provides for online registration and provides the insurance exams at multiple testing centers in Washington. The biggest bit of advice we can you give is to try to schedule your exam several weeks in advance. This does a couple of good things. First, it lets you put your study plan of action in place and provides an incentive to stay on track. Second, you want to make sure you have a spot when you are ready to take the exam.
If you need to change your date, that is normally not a problem, but you should do so with enough warning to avoid a penalty. The Licensing & Testing tab on this page provides you with succinct directions.
Go to the PSI Exams website to schedule your exam.