Comming from Snohimish or Pierce county, the easiest way is via Interstate 5. Form the south you can also take State Route 167. Comming from the east you can take Interstate 90, or US Highway 2.
Seattle-Tacoma International Airport, (Airport code: SEA), called "SeaTac" by locals, connects Seattle to all regions of the world, with especially frequent transpacific routes. Alaska Airlines provides something approximating discount air fare to and from the San Francisco Bay Area and Southern California.
Buses in downtown Seattle are free between 6am and 7pm in the downtown core of Seattle. Just get on and get off. To read the details refer to Metro Free Bus info.
Sound Transit (diesel and hybrid buses, trains) is more expensive, but has many convenient express routes that travel South (to Tacoma), East (Redmond, Bellevue), and North (Bothell, Lynnwood).
Sound Transit Sounder light-rail service.