Coming from Snohimish or Pierce county, the easiest way is via Interstate 5. Form the south you can also take State Route 167. Coming 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.
Metro Transit (electric or diesel city buses) actually works pretty well. The web trip planner is straightforward and accurate, as long as your bus is on time.
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).