Yellow metro line to L'Enfant Plaza metro station (4th stop from DCA). Walk outside and take bus 5A which will take you to IAD. Metro takes 15 minutes, bus will take around 90 minutes. Make sure you time it right because only one bus an hour. $.45 for the metro, $3 for bus. Make sure you have exact change for bus because they will not give you change.
Edit: The bus is also available from Rosslyn metro station but its first stop is L'Enfant Plaza so you will have a better chance of getting room for luggage and a seat.