The AC Transit (http://www.actransit.org/) bus system service is a good way to get around if you're headed for downtown Oakland, Jack London Square, the Grand Lake district, or Temescal. Otherwise, depending on where you're going, it can seem like you're waiting for a long time for the bus to arrive. The AC Transit costs $2.10 for adults. Add $0.25 for transfers. BART provides easy access to the Downtown, Fruitvale, and Rockrdge areas, and makes for an easy day-trip from San Francisco. The last return train runs at about 12:15AM.
BART has 8 stops at major areas of visitor interest, which makes it perhaps the best way to experience Oakland. A majority of these stations are adjacent and of walking distance to popular neighborhoods, eliminating car and parking hassles. BART stations are usually named after the neighborhood they are located in. For example, to visit the chic Rockridge neighborhood, exit the Rockridge BART station, conveniently located steps from this area. Same goes for the Fruitvale District Fruitvale BART station. Lake Merritt BART station is only a block away from the Oakland Museum of CA. Chinatown is 3 blocks from the 12 Street/City Center BART station.
Those hoping to go to the hills of Oakland are probably best off in a car, as bus service to these areas is sparse.