The listing says it's only 2 blocks to the Brookland Metro Station. Walk there.
Then the quickest way would be the Red Line to Gallery Place. Change to the Yellow Line. The Yellow Line will take you straight to DCA.
An alternative--if they're doing track work, for instance--is to take the Red Line to Metro Center. Then transfer to the Blue Line going in the direction of Franconia-Springfield.
Here's a link to the rail map: http://www.wmata.com/rail/maps/map.cfm?
According to Metro, it should take 27 minutes. I'd allow at least 40 minutes. The fare is $2.70 off-peak or $3.45 peak.
Of course, you could also take a cab. That'll cost about $22.
Hope that helps.