First of all, after you get your resume and other professional data together, register at job searching engines like Monster, Seattle Jobs or Career Builder, they have great requests from employers therefore they can really help you get targeted job. You can also give Washington Jobs a try as they are one of the best of the lot. Science jobs Seattle & night jobs Seattle have much recruitment therefore if you are looking for one, you might get it from there. Searching Craiglist classifieds is also an option but it is more time consuming and also you have to personally contact the employer which is automatic in the case of above mentioned websites.
Other than that, you can call the Seattle unemployment agency, whose aim is to find targeted jobs that suit your qualification and get you the best pay. Give them you necessary details and you are on the right track. Contact them frequently to get the updates. You can also register yourself with some of the local listings and get the opportunities from there. There are many Seattle jobs classifieds online, some of them are good, most of them are very limited, therefore select the reputed website to post your resume onto.
Nevertheless, if you have friends in Seattle you should call them and ask them to hook you up with a job using their contacts; they will help you get an idea of How to Job Search in Seattle offline.