How would I get from BWI Baltimore Airport to the Pentagon by public transportation?

Metro! There's a Metro stop right at the BWI arpt and another one at the Pentagon
http://www.stationmasters.com/System_Map/system_map.html

I have two answers for you, depending on whether you are arriving during a work day or not.

First - this should work any day - you can take Metrobus B 30 from BWI Airport Stop 1 to the Greenbelt Metro Station, then get on the Green Line. From the Green line transfer to the Yellow Line (you can do this at Ft Totten - which is the first stop where they merge, but it is possible all the way to L'Enfant Plaza). Yellow Line will take you to the Pentagon Metro Station.

The other alternative is to take the MARC Penn line from BWI to Union Station. At Union Station you need to get on the red line toward Shady Grove for 3 stops, and at Metro Center change to the Blue Line, which goes to the Pentagon. You could also switch to the yellow line at Gallery Place/Chinatown (which is 2 stops) and take the yellow line toward Huntington.

MARC Trains only run Monday to Friday, during Business Days.

BWI and Reagan National Airport both have METRO STOPs unlike Dulles International Airport which is in the near distance future planning when they extend the Orange Metrorail past Tysons out to Dulles.

The Pentagon of course is the Northern VA hub that has Metrorail and public bus widely available.

Next thing to consider is location of lodging to/from Pentagon that has Metrorail access is rather economical and in safe environment.

Best of Luck!

The person who said the BWI has a metro stop is completely wrong, there is no metro going to BWI. There is, however, a train station. Your two options are to take the train to union station or take the bus to the greenbelt metro and then go to the pentagon metro station from there. Regardless of the day, I would recommend taking the bus. It's much cheaper (last i checked between $3 and $4), very reliable, and I think it's easier to get to pentagon from Greenbelt then from Union Station.

To find the bus, go outside to Ground Transportation and just ask someone for the bus to Greenbelt. There are usually a couple people waiting around for it. Once you arrive at the metro station take the train south (it's the end of the line so there's only one direction) all the way to L'enfant Plaza. There you need to get off the train, and wait for a yellow line trian to come and pick you up. It runs on the same track so you won't have to go anywhere. The yellow will take you across the river to pentagon.