I'm an architect in San Jose and I've had experience doing this on a few homes around here.
First, it is an expensive and timely process, but in certain areas can be well worth it. That's especially true if you are already at the maximum floor area ratio (FAR) of .45 in San Jose for your property. A full basement gives you extra square footage that is not included in that FAR calculation.
The new basement will have to comply to all of the current building codes including ceiling heights, egress (exit) wells, stairs and possibly a sump pump/sewage ejector. Also, the new basement which will be the new foundation for the house will need to have hold downs that anchor the wood structure of the home to the foundation.
As far as cost: expect to pay somewhere in the range of $100 per square foot for the unfinished basement and considerably more if you finish the basement and add a bathroom, etc.
While the foundation is being built, the house will be raised on a few steel beams. It's precarious and if a large enought earthquake happens during that time, you may lose the house. It's a real nail-biter sometimes and the house may be raised like that for three months.
Hope this helped,
Jennifer Kretschmer, AIA