Many people arrive in Seattle vs Vancouver since it is priced cheaper than flying directly into Canada.  Please read the article trips into Vancouver and Victoria to answer many of your questions on driving or taking the ferry to Victoria before asking a question.  This is for the common forum question of specifically how to get to the Vancouver cruise ship docks from Seattle.

Driving is, of course, one option, but not highly recommended.  Drop off fees are substantial and if you are Canadian, you are not allowed to bring a U.S. rental car across the border.  This doesn't apply to U.S. residents but you need to make sure you have permission from the rental car firm to cross the border.  Waits at the border can range from 20 minutes but waits of 2hrs or more are not unheard of in summer. 

There is a good web site that shows, graphically, the best and worst times for crossing the border, both north and south bound. It also breaks them down by season: www.wsdot.wa.gov

There is currently a morning train and a evening train to and from Vancouver.  There have been talks about adding a mid day train but for now its just a rumor.  Keep track by checking Amtrak.com.  If the train leaves too early or it doesn't work into your plans then taking the Amtrak bus is another alternative.  It leaves from the train station in Pioneer Square in downtown Seattle.  It would be about $30-35 via  cab from Seatac.  The advantage of the bus is that it goes directly up I-5 and makes no stops except at the border.  From downtown Vancouver its a short cab ride to cruise ship docks

once in Vancouver its only about a $15 cab ride to Canada Place.  There is a shuttle service but normally the cost of a cab would be the same or less, however if lots of luggage or with a group the shuttle may work better.

http://www.seaandskishuttle.com/

Light Rail has begun from Seatac into downtown Seattle.  The Amtrak station is one block from the entrance to the bus tunnel.  That is another option to get to Seatac.  From baggage claim at Amtrak turn left and go thru the Qwest Field Parking lot.  You will see an elevator.  Take that up a floor and cross the street.  Once you get to the other street turn left and you will see the turqouise entrance to the bus tunnel.  That will take you direct to Seatac for $2.75


The other service available is a coach service called Quickshuttle.  It serves Seatac ariport, downtown Seattle, Vancouver airport, downtown Vancouver and Vancouver cruise ship ports.  Logistically its very good as you can leave right from the Seattle airport.  The downside is the service is more expensive and will make many more stops on your way to Vancouver.  It is however very logistically easy.

There are two better motorcoach options that make far fewer stops than Quickshuttle.  

 

Boltbus.com

is operated by greyhound and offers very low fares direct to Portland or Vancouver BC.  The 'stop' in Seattle is right in front of the bus tunnel in the International District so if you do take light rail into Seattle you'll be in the right spot.  

The second option would be to take the Amtrak Bus.  The advantages to both Bolt bus and Amtrak is that they only stop at the border, then go right into downtown Vancouver, both stopping at Pacific Station.  This is perhaps a $10 cab ride to cruise ship dock so these are very good options.

 

taking the regular Amtrak train is still the best as it follows the coastline, is very scenic, and avoids any delays at the border.

 

Another possibility is to fly using Alaskaair.com from Seatac.  If you book in advance or look for web specials sometimes the airfares are just a little higher than other options.

If you have a few extra days taking the victoriaclipper.com from downtown Seattle to downtown Victoria is very easy to do.  Once in Victoria you can sightsee for a day or so then take a bus to Vancouver from Downtown Victoria.  This is very easy to do by using Pacific Coachlines out of Victoria or Vancouver.  The website is pcl.com.

Hope this helps.  If you need more help please post on the Seattle forum.