The distance between the airport and Seattle city is around 13 miles and that between the airport and Tacoma is 20 miles.
There are different modes of transport available from airport to different parts of Seattle and Tacoma:
http://www.airwise.com/airports/us/SEA/SEAtran1.html
Cars: Cars are also a comfortable mode of transportation. The distance between the SeaTac airport and south of Seattle city is close to 13 miles and the distance between SeaTac airport and Tacoma is 20 miles. The time that takes on car from the SeaTac airport to Seattle is approximately 20-30 minutes and to Tacoma, it is 30-0 minutes.
Taxis: You can also use taxi services in order to travel from and to the SeaTac airport. The taxis are available on the third floor of the parking garage at the airport. The taxi fare USD 30 when traveling to Seattle and it is approximately USD 35-40 when traveling to Tacoma.
Bus/Van: You can also use the Airport Express Bus service for commuting purpose. The departure of these buses is at an interval of every 30 minutes to several area hotels. These taxis leave from outside the baggage claim area. There are frequent bus services available to downtown Seattle. The Sound Transit bus has frequent services to Downtown Seattle.
http://www.portseattle.org/seatac/ground/shuttlebus.shtml