The MARC Train is a commuter rail serving numerous locations in Maryland and Washington DC. The MARC Penn line runs between Union Station in Washington DC, Baltimore, and points north, to include a stop near BWI.
To get to the MARC train, you need to catch a shuttle to the BWI Amtrak Station. These shuttles are located outside baggage claim and run approximately every six minutes (theoretically - I've definitely waited longer) except between the hours of 1:00 a.m. and 5:00 a.m. when they operate every 25 minutes. The shuttle drops you off right at the station. Be aware, for the trains to Washington DC, you will need to use the elevator (or stairs) to cross the tracks.
Once you have arrived at the train station, but before you cross the tracks, be sure to buy a ticket - a one-way ticket to Union Station costs $7, but if you buy the ticket onboard, it will cost an additional $5. You can either go to the counter or use one of the machines, if you use a machine, make sure to select MARC tickets - Amtrak tickets are often much more expensive.
Once at Union Station, it is an easy transfer to Metro, if necessary. A trip between BWI and the Farragut North Metro Station downtown taking the MARC train takes about 80 minutes, and costs between $9 and $9.25.
MARC Train - Timetable
For the Amtrak, follow the same directions, but but a ticket and board an Amtrak Train. It also takes you to Washington Union Station. It will save you about 15-20 minutes on the train, but will likely cost you starting from $14, but can often cost more than $30. For prices and availability, please go to www.amtrak.com.