Study a map, then give yourself over to a few days of trial and error. Lost The city's big, but not that big, and you can learn your way around it in no time. The best way is just to get lost in it once or twice, and the general scheme of things will materialize. Even if you don't live in the District, try starting with a walking tour. Washington is a walking town.
Residents are accustomed to it, and tourists learn it soon enough.
Use landmarks to orient yourself, and note where the nearest Metro stations are along what will become your accustomed routes. Then try public transportation. Metro buses are an inexpensive way of getting the lay of the city.