Dulles to Mall
 

Not going for the inaugural but generally, what is the most economical way to get from Dulles to the Mall area. Do any hotels offer free shuttle service?

There are shuttle buses that take you to the West Falls Church metro station where you can get on the orange line right to the Mall. Where will you be staying? I don't think any of the downtown hotels would offer free shuttles all the way out to Dulles.

Most economical would be the 5A bus.

http://www.wmata.com/bus/timetables/dc/5a.pdf

Airport websites usually offer ground transportation info. There is also another bus for about $9 (I think) called the Washington Flyer or something

Metrobus 5A is the most economical way to get from IAD to the Mall area. It stops at L'Enfant Plaza which is an easy walk to the mall.
Depending on time of day and traffic the bus can take up to an hour travel time.
http://www.wmata.com/bus/timetables/dc/5a.pdf

And we have the reverse commute in the afternoon, so traffic inbound inside the beltway can be a hassle later in the day.