Originally Posted by marinedjp
MARC Train it. 6 bucks each way, there is a free shuttle from the airport to the train station across the street. Its between 25-45 minutes on the train into DC and it takes you right into Union Station.
You can view the schedules at mtamaryland.com and click on Marc Train.
It does not run on weekends, you would have to take an Amtrak train.
I agree that the MARC train is the best way if you're not driving, but it is bad that it doesn't run on weekends. The Amtrak train is much more expensive than the Marc train. If you want the cheapest transit, there's a Metrobus that runs from BWI to the Greenbelt Metro station 7 days a week, and then you can take the Metro downtown.
http://www.wmata.com/timetables/md/b30.pdf
Hopefully you'll arrive on a weekday. The Marc trains are quite frequent and fast.