There are many ways to get from the airport to the pier in Seattle
The most expensive way to go is by taxi unless there are four of you
You can also get a bus shuttle from the airport to a downtown hotel and then take a taxi to the pier
You can also take Shuttle Express which will let you off at the Pier -
If you are really cheap and crave adventure - there are public buses that go from the airport to downtown and you can transfer to the streetcar which will get you near the pier. If you have lots of luggage - probably not such a great idea.
If it was me and two people - I would do the Shuttle Express - they charge a few dollars more for the second person when we use them to go to the airport