I'm going to have to ask my local readers to bear with me here, but there's some important info I haven't shared yet with our out of town guests.
I think, by now, most visitors have gotten the word about not driving to the National Mall. It's possible, I guess, and people do it, but you're more likely to see Obama than find parking anywhere close to the Museums. And, to indulge in a tangent for a second, if you are that lovely couple from New Jersey who decided to take do it yourself parallel parking lessons in front of the Smithsonian, than let me tell you that the bus honking at you was mine. I got to ask you, what made you think the parking fairy was going to help you on the 16th try? There's no shame in not knowing how to parallel park, there is in blocking traffic for half of downtown DC.
Whew, now that that's out of my system, let's focus on some actual useful advice. Everyone always says "take Metro to the Smithsonians" and folks naturally assume that the Smithsonian stop is the one to get off of at. However, the "Smithsonian" is a gigantic institution that sprawls from the base of the Capitol to the shadow of the Washington Monument, well over a mile in distance. Due to the proximity of several Metro stations, the Smithsonian station may not be your best stop.
Much depends on what line you are taking to the Mall. Consult your friendly Metro Map, first. The Blue, Orange, Yellow, and Green lines all cross under the Mall. If you are taking the Yellow line into the city, for example, it does little good to get off L'Enfant Plaza, wait ten minutes for a transfer to the Blue/Orange Line, get off at Smithsonian if you are, in fact, going to the Air and Space Museum. So, let's break it down by museum.
View Metro to the Mall in a larger map
American History: Get on the Blue or Orange Line and get off at Federal Triangle or Smithsonian stop. The Museum is slightly closer to the Smithsonian stop, but I prefer the Federal Triangle stop, especially if you have to push a stroller through the gravel of the Mall walkways. If you get off at Federal Triangle, when you take the escalator to the top, turn around, walk to 12th St, and take a right.
Natural History: If you are coming from the Blue/Orange line, then the same as above. If you have a stroller or wheelchair, I'd recommend using the Federal Triangle stop. The Constitution Ave entrance that you come to is handicap accessible, in a way that the Mall entrance very much is not. If you are riding the Yellow or Green Lines, you might want to save a transfer and get off at Navy Memorial/Archives. Upon exiting, walk straight to 9th street, cross Pennsylvania Ave, and walk south one block. The Natural History Museum will be across the street.
Smithsonian Castle, African Art Museum, Sackler Gallery, and the Freer Gallery: These are all readily accessible from the Smithsonian station. Use the Mall exit.