Originally Posted by inlogan

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.