Yes, catch the Green Line at either the Greenbelt or College Park - U of MD stations. You will need to get a re-loadable card for each passenger. Metro eliminated paper cards.
Get off at the Archives Station, across from the National Archives and National Gallery of Art (NGA). Also, closest to Smithsonian National Museum of Natural History and National Museum of American History.
Or at exit L'Enfant Plaza, just a few blocks from the Smithsonian National Air & Space Museum, Museum of the American Indian, and Hirshhorn Museum.
Here is a pocket PDF guide to DC Metro.
Feel free to ask any specific questions. I commute to the National Mall by Metro every day, though on the Orange/Silver Lines.
