Hi,
For a city its size, Seattle's public transport is quite disappointing. There is a bus system which is quite OK if you work downtown and live on the West side of L. Washington, but if you have to go farther afield or across the lake it's a royal pain. You can see the bus plan at the following website:
http://transit.metrokc.gov/
The ferries are an option. Again, it's pretty easy if you work downtown and live on Bainbridge Island, but otherwise you're looking at a drive on either end.
Finally there's the train. There's a commute rail line that goes from Tacoma to Seattle and another line that goes from Everett to Seattle. Whether the train stops in places you'd want to live is another matter. Not for me, thanks. See:
http://www.soundtransit.org