There's two types of rail that you'll potentially be dealing with - Light Rail and Commuter Rail.
Light Rail (MTA) can be used to get from the Airport terminal to the Inner Harbor/Camden Yards area - about a 30 minute ride. Depending on which Hotel you're staying in, it can be used to get from the airport to your hotel. If your hotel is more "Harbor East" it would probably make sense to cab it, given that you've got a week's worth of luggage with you. The cost per trip of this service is $1.60, though a $3.50 day pass is also available that allows you unlimited rides on all MTA local services.
Commuter Rail (MARC) is the service between Baltimore and Washington DC. The ride is about 50-60 minutes. The service consists of two lines - the CAMDEN line which is more convenient to the Harbor, but as Prankster mentioned, only runs in peak hours (5-8am) (3-6pm). If you prefer to sleep in late, the PENN line operates all day long until the late hours, but is a couple of miles from the Harbor. It is still convenient however, you can easily walk to Charles and Pratt Street and catch the #3 bus up Charles St. right to the front of the station. When you return, St. Paul street houses the #3, 61, and 64 buses that all go back to the harbor - or if you prefer, use a cab. Bus fare is just like the light rail - $1.60 per trip - IIRC, MARC round trip fare to DC is $14.00.
Enjoy your stay - Go Birds!