There's nothing wrong with being a tourist; when I'm done with crazy tourist season here in DC, I hope to be one elsewhere myself. But if you'd rather not scream it from the rooftops, here's a few easy ways to avoid standing out when riding the Metro:
1. Walk on the left, stand on the right: Officially, Metro feels that its escalators are not designed for walking, so for liability reasons, they've long resisted making this clear. Much as I should eat vegetables and exercise more. But back in the real world, there is no quicker way to incur the wrath of a Washingtonian than standing on the left. To us, it's not just a quirk, it's rude. We even make t-shirts about it. So please, help me out on this one. It just takes one person to make the whole system grind to a halt and make everyone hate tourists. Then my friends blame me. And then I have to buy my own beer. And I don't like that.
2. Don't stop in front of the doors/bottom of escalator/past fare gate/etc.: It's perfectly natural to experience a sense of bewilderment as you make it through the next step in the system. It's a complicated system and new for you, and no one expects you to quite know where you're going. But if you step out of the train, stop, and look around in puzzlement; everyone behind you is piling up like keystone cops. Walk a few steps and then get your bearings.
3. They're not elevator doors: The train doors do not re-open if you put your arm in them. We'll put aside the rudeness of keeping 700 people waiting because your group is strung throughout the station; if you break the door trying to hold it open, the train has to be put out of service and everyone has to disembark. If that happens, forget about buying me beer. At that point, my friends march on my house with pitchforks and torches.
4. Have your exit fare ready: People are generally ready going into the Metro, but it's not intuitive that you need it when you exit. Be prepared, and have your card ready to go when you get to the gate. This is why I recommend a SmartTrip Card; you don't even need to take it out of your wallet. You can just swipe the wallet.
5. Don't be afraid to ask directions: Everyone is hustling around and looks so serious. You may feel alienated and that everyone is being rude to you. They're not, they're just on autopilot as they shift from home to work and back again. Most of us are happy to help visitors out, especially if they've shown a little courtesy by following the above rules. A lot of us love living here, and are secretly eager to show off our little hints and tips. Sure, we have a few people who are just anti-social, but the average person on the train will be glad to help you out a bit. And if they don't, just smirk, and mutter "they must be new here" loud enough for them to hear you.