You can get a free airport shuttle to the Amtrak station, where for $5 you can a ride a MARC train (Maryland commuter rail) into Union Station. You could also take Amtrak, but I believe it's more expensive. From Union Station, either take the Metro or catch a cab to your hotel.
Edited because METRA is in Chicago, not Maryland (thanks to dhacker for catching my slip)
[This message has been edited by warmsnickers (edited 09-15-2002).]