If you look anywhere, you'll see that there are three commercial airports that service the DC area. Ronald Reagan Washington National Airport (DCA), Washington Dulles International Airport (IAD), and Baltimore/Washington International Thurgood Marshall Airport (BWI). Having three airports in the area makes getting anywhere in the country, or even outside the country, a reasonably painless process. But beware -- the airports are by no means created equal, in terms of cost or convenience, so it's worth some discussion about which to choose and why.
DCA goes by the name Regan or National, depending on how long the person you are talking with has been in the area. It is by far the easiest airport to get to (the Blue Line of Metrorail goes directly to it). It's also the smallest of the three airports, and because of its convenience and size, flights tend to get expensive quickly (so book early). Despite the monetary cost, it's worth weighing the time and cost involved in getting to the DC area airports when searching for flights. If you're taking the 5A Metrobus to Dulles, for example, you'll be looking at $12 and an extra hours of travel time. These implications may tilt the scale toward Regan despite cost.
IAD, know as Dulles, is the largest airport in the area. It is a hub for United, and has flights pretty much everywhere you could want to go. Unfortunately, though, Dulles is located 26 miles west of DC, and without a car or a ride from a friend, it is less than trivial to get to since Metrorail doesn't get there (not yet; the Silver Line, under construction, will end up connecting IAD with the rest of the Metrorail system). A list of ground transportation options is available here.
If you have some time to spare, and are traveling during its hours of operation, taking the 5A[pdf] Metrobus can be the most cost effective way of getting to the airport (downfalls are the 40-60 minute trip and the once-per-hour schedule). In my experience, a taxi will generally be in the $50-60 range; pricey for an individual, but okay in a group of 3 or 4. The SuperShuttle is another viable Washington Dulles airport transportation service, in which you travel with of group going to nearby destinations for a reasonable per-person price, so it's better than a taxi for an individual, but worse if you're traveling with others.
BWI is 30 miles north of DC, and is the most difficult of the airports to get to. It is a hub for AirTran, and a major airport for SouthWest (which can be a big plus). It is also often the cheapest place to fly into or out of (but not cheapest for getting to on the ground from DC in terms of time or money). BWI airport ground transportation options can be found here. Most options are similar to those at Dulles.
One option is to take the Metrorail's Green Line to Greenbelt Station, and then take the B30 Metrobus to the airport. This works fine, but can be a long process, depending where on the Metrorail system you start. Another good option is the MARC train to and from Union Station (accessible by Metrorail). Check the schedules before you make your choices. I found out the hard way, that the MARC doesn't run Sunday nights, and the Amtrak was a 40 minute wait. Fortunately, I was able to grab a taxi with others in the same situation.
A taxi to or from BWI, in my experience, can be $75 to $90. Again, this can be okay in a group, but would be steep for an individual. During heavy traffic the trip can take a long time (so make sure you build in an extra hour), but with no traffic it's not too bad. Again, the SuperShuttle is an option which can be practical if you are an individual traversing to DC.
If you have any other tips for flying into or out of DC, leave a comment and let me know. Hopefully this helps you plan your trip!