I have never actually gone from SFO to OAK via BART or v.v., but I have gone to and from both airports using BART many times, to/from various places in the Bay Area (including SJC!).

The station at SFO is built into the airport and finding it is pretty straight forward. The BART station can be reached on foot, or you can avail the service of the people mover, which is also called AirTrain but only runs within the confines of SFO unlike its namesakes at EWR or JFK.

Check:

http://bart.gov/guide/airport/airport.asp

for more info about fares and if you will have to change trains along the way.

(The BART system is like Washington's Metro in that fare is based on distance travelled, and you'll have a fare card that will be used to enter and exit the system and will have to have at least the amount of the fare on the farecard to get out.)