In addition to Sea-Tac airport and taxi/limo or rental car, there are:
Commuter rail service (http://soundtransit.org/x...) from Tacoma to Seattle and back, with the majority of trains running to Seattle in the morning and to Tacoma in the evening.
A ferry to and from Vashon Island (http://wsdot.wa.gov/ferri...). Don't plan on walking anywhere when you get to Vashon Island; you'll need a car to get anywhere worth seeing. Some people bike around the island, but be prepared for major hills. You can continue to Seattle or Port Orchard by crossing the island to the other ferry.
Amtrak Cascades trains (http://amtrak.com/trains/...) running between Vancouver, British Columbia Canada and Eugene, Oregon, stopping in Tacoma. Amtrak (http://amtrak.com/index.html also has trains that go to California and to points east, from Tacoma.)
Sound Transit buses from Seattle, SeaTac, and Lakewood (http://soundtransit.org/x...)
Intercity Transit buses from Olympia (http://intercitytransit.c...)
