Click on the image to enlarge
You can download or print a free copy of the Washington, DC Metro map here.
I know that subway maps can seem complicated, but trust me, this one is fairly easy to navigate. Most of the time you will be using the Orange or Blue lines to navigate the city, but if you get lost just ask one of the locals for help.
A quick tip: If you want to know which direction the train is going just look at the writing on the sides. It will say the last stop. So, on the Orange line if it says Vienna/Fairfax-GMU then the train is going West towards that station.
Also see:
Washington, DC Maps
A list of different downloadable free maps
A Train Arriving at a Metro Station
See a video of what the inside of the stations look like