Getting around is easy and affordable, with a number of public transit options. Get a guidebook, preferably one that offers transportation advice and sample walking tour itineraries. There's a lot to see, and a good guide can help you figure out where to start. See the city on foot.
Most local attractions are within easy walking distance of each other.
Use the Metrobus and Metrorail of the Washington Metropolitan Area Transit Authority. Take the Tourmobile. This system isn't as cheap as public transit, but it's a convenient option. Tourmobiles shuttle visitors around to all the major attractions, including the White House, the Supreme Court, the Capitol, the war monuments, Arlington National Cemetery and the major museums. Ride a bike.