The best bet I think is to fly out of OAK (about the same distance from San Fran as SFO) using Southwest Airlines (LCC @ southwest.com). Refundable/changeable tickets are about $99-$125 one way and you can get there using BART (mass transit) I dont think the train idea will be much cheaper using Amtrack which leaves out of Emeryville (other side of the bay from San Fran) and its several hours, same by car or bus. Ive driven back from LA to San Fran and it was near 8 hours..not a great drive either. You can check Greyhound (bus lines) to see options there but I would vote for Southwest out of OAK to LAX. Lots of flights and as close to a bus as it comes.
There are other airports in LA area including Orange County SNA (Alaska, Southwest, UA, AA) and Jet Blue flies from OAK to LGB, Longbeach. American, Alaska and United do fly out of SFO to LAX but my guess is the fares will be a bit higher and may be non changeable except for fee which these days is $50-$100 if not more.
If you have time, try to get to the Marin Headlands, across the Golden Gate bridge, great views and hikes. Also further north are the great Redwood trees, at Muir Woods. Try the slanted door restaurant on the Embarcadero Ferry Terminal building, asian fusion cusine and my fav cheap burgers at in-and-out burger near Giaradelli building. Good luck.