Chinatown is in downtown San Francisco, approximately bordered by Powell Street, Kearney Street, Columbus Street, and Bush Street. It is not hard to get to using public transportation, BART and Muni stop near or in Chinatown. Chinatown is just a bunch of random streets with no central attraction to head for making it difficult for tourists to figure out what to do! Either you'll love that or you'll hate it. If that doesn't sound like your cup of tea, you can safely skip the area and not miss out on anything major.
Head for Portsmouth Square or Grant Avenue and you'll at least get a taste of the area. For an even better taste, find a hole in the wall dim sum restaurant and enjoy an authentic lunch. Or just go to the Golden Dragon on Washington Street if you don't feel like taking your chances. In 1977 a shootout between the triads took place at the Golden Dragon.
Other than that the main attraction is shopping. One thing for the tourists to keep in mind, Chinatown is cheaper than the other major tourist areas, get your San Francisco items there! Visit the various small shops and markets in the area and pick out that one of a kind souvenir to take home with you. The most noteworthy are the Chinatown Kite Shop, the Wok shop, and the Golden Gate Fortune Cookie Factory.
Below are various pictures of Chinatown, click to enlarge.
The Grant Avenue Gate into Chinatown (Above).