How to get to/from Washington Dulles International Airport?

Can you wait a couple of years? They're extending the DC metro to the airport at the moment... The metro should reach Tyson's Corner in 2013, and the airport a few years later (2018 is apparently the latest date).

If you don't want to wait several years, it all depends how much of a hurry you're in, and when you're going. During peak hours, your best bet is to take the bus between the airport and Rosslyn metro station, and the Orange line between the city and there. Traffic can get really bad on the freeway at peak times, so you can smugly speed past it on the metro. The bus ticket is $6 (exact change only), metro onwards is a few dollars depending on your destination, and the 5A timetable is here. I've done this myself, and I found it fine, even with a moderate size bag.

However, because of the work to extend the metro, evenings / weekends can see a lot of engineering work taking place on the Orange metro line. For those times, you'll be better off taking a bus from downtown to the airport. There are both private and public ones, with differing costs / comfort. The MWAA site lists the various options

From next year, I think the best bet will be bus to Tyson's Corner, then the new metro line into town.

When I was there last I used SuperShuttle. Its dead simple (just walk to their counter) and reasonably priced at about $30, if you are traveling in a group, additional passengers cost $10. Compared to taking a cab by yourself or with one other person, this saves a bundle.

Of course it is a shared shuttle service so it will take a bit longer than a cab ride, but it will get you all the way to your hotel. The only cheaper alternative is to take the bus to where the metro ends and take it into town. This will be cheaper but will likely take longer, especially if the metro does not stop close to your final destination.