The easiest way is to take a taxi. We're not just saying that because we're lazy and we take cabs everywhere. We're also saying it because we get commissions from
Red Top Cab Company. Just kidding! If you do take a taxi and want to pay by credit card, please make sure that your cab driver takes credit card before you get in! From Reagan to the Westin Georgetown should be ~$20 and from Union Station to the Westin is ~$15. From Dulles to the Westin is anybody's guess, try about ~$60, but don't quote us on that.
If you're coming from Reagan Airport or
Union Station (where Amtrak drops off), you can also take the local
Metrorail train. The Metro is DC's version of the New York subway or the London Underground, clean and without big rats. There is a price for cleanliness. Do not eat or drink in the Metro. And if you do, don't call us to bail you out when the Metro police lock you up. We'll be at the alter, remember?
From Reagan, take the blue line train in the direction of Largo and transfer at Metro Center stop to the red line heading in the direction of Shady Grove. Get off at the Dupont Circle stop and start walking! Alternatively, you can take the yellow line in the direction of Georgia Avenue and transfer to the red line at the Chinatown metro stop. Proceed towards Dupont Circle.
From Union Station, take the red line train towards Shady Grove and get off at Dupont Circle. Start walking!