Public Transportation: From DCA, take the Metro Blue line to Rosslyn, then transfer to the Orange Line. Take the Orange Line to West Falls Church. From there, you can take the Washington Flyer Shuttle to IAD for 9 dollars. Including the Metro fate, the total cost should be about $14. Total time is usually 75-90 minutes.

Many locals park at DCA, and take SuperShuttle to IAD, so this is another option, and the fare will probably run you around $30.

IIRC, taxi fare from DCA-IAD is around $55-60