If you are new to the USA or Seattle transportation is a challenge. Much of the growth of Seattle and its "bedroom" communities has taken place in last 40 years and transportation is around the Single Occupant Vehicle. Retailing moved from downtown Seattle out into suburbia with its "strip malls" and mega shopping centers. In last 15 years Biotech and Software businesses established themselves in downtown Seattle. The under 30-year-old technology professional then created the housing and public transportation demand downtown Seattle. The different regional governments launched projects to resolve the shortage of transportation with little coordination and limited effect. When you compare Seattle transportation too centrally planned European public transportation there is no comparison.
When you arrive at the Airport near Seattle you have two options for transportation the first one is a cab which can cost $40-60 dollars the other option is the new Light Rail to downtown which is $2.75. The Light Rail is good if your destination is downtown.
Word of caution just like any large city do not look confused the city is safe but panhandling is pervasive and goes from very aggressive too sad. Mental Institutions closed and patients went to the streets. It is all very sad but you cannot change it so avoid eye contact or hesitation if you feel like you need to help look for the "authorized panhandler" selling a daily magazine "Real Change" and $1.00 and above is proper.
The bus service is very good until 10:00 PM a good example is Alki Beach which is cleared by police at 10:00 PM and you cannot find a Bus. The bus is low cost $2.75 will get you anywhere in Greater Seattle Area the low cost also attracts many homeless people and often they have “no boundaries” so be prepared to move or stand.
You cannot get a Taxi by raising your hand you will need to call the Taxi Company. Make transportation part of your adventure I have put together this video of many of your transportation options from Airplane to Seaplane, Rail to Light Rail and SOV to HOV