Go to door 4, on the arrival level, at IAD and buy a ticket on the Washington Flyer Coach Bus. They leave at :15 and :45 past the hour with direct service to the West Falls Church Metro station. The ride takes 20 minutes. If you are an airline employee, show your ID for a discounted ticket. Take the orange line towards New Carrollton (only one available) to Rosslyn and transfer to the Blue line towards Fanconia/Springfield. Trip from West Falls Church to DCA takes right at 30 minutes including transfer. To transfer at Rosslyn, get off the train and take the escalater to the lower level. At times the blue line train comes in on the lower track within a minute or so of the orange train. So as not to miss the connection, I've found it best to get on the orange train somewhere in the middle. This will put you directly across from the escalator at Rosslyn.
Stickn