Washington are proud of their subway system, which they call Metrorail or just metro. It is much more modern than New York's. This is quite natural as it was opened only in 1976.
Instead of a token, you use a magnetic fare card, which you buy from vending machines in the stations. To get to the platform you must insert your fare card at the entrance gate. The card pops out with the time and location encoded. At your destination you insert the card at the exit gate and the fare is automatically deducted.
Buses connect all Metro stations. They also reach areas of Washington not served by the Metro. You can get a free transfer ticket from the Metro to a bus from a machine in the station where you begin your trip.