Ok, so you're at the national mall, right? Find the bunch of signs that say "Smithsonian" with a big blue M on it. Go down the flight of stairs there. When you get to the bottom they will have these vending machines that sell "Smart Rip Cards." Buy one and put money on it.
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Now swipe your metrocard and follow the blue signs that say "Largo Town Center" and ride the blue/orange line train for ONE STOP. Then make your way to the yellow line that says "Huntington." Get on the yellow train and ride until it says "King St." Make sure you get on at the front of the train, and you'll get some great views going over the Potomac. You'll now be in Virginia. Phew. That was a close one.
Get off the subway and start walking towards the river. After about a mile you'll be getting close to the water. Go all the way to the water, and find the water taxi stand. Buy one way tickets to "Georgetown." Since you probably spent half the day figuring out how to get to the national mall (w/o using public transportation) it'll probably be lunch time, so buy your ticket for 2 hours later and then walk back towards the subway. There will be a lot of fancy places to eat here. Don't eat at night unless you carry gold bricks in your wallet.
If you finish eating early you can explore the pier/park around where the water taxi service is.
Board the water taxi to Georgetown, and enjoy the views of all the cool shit you aren't supposed to see like secret research naval bases and the other side of the Pentagon.
Get off at Georgetown. Georgetown is the only part worth seeing in DC, as evidenced by the location of the Swedish Embassy to your right. The Scandinavians have a habit of stealing the best places. Enjoy.