In California is it legal to build and operate a still for the distillation of homebrew?
No, it is not legal to distill alcohol in the US without a license.
It is possible to obtain a license for small batch production. See the discussion forums on the American Distilling Institute web site for information on the steps required to license a microdistillery, from people who have done it.
The concensus of opinion seems to be: it's not difficult to get the federal license even for small production. The federal license is basically a permission to pay taxes, and what "revenuer" would refuse a new source of revenue, no matter how small?
The main thing seems to be to know the application process and to not rely on government web sites for information, since most of them basically say "Go away".
You're more likely to have difficulty getting local building permits to build or retrofit an existing structure to house the distillery. Federal regs require that the still and fluid processing and storage must reside in a structure that is not a place of habitation - a free standing garage or shed might work, but not a basement or attached garage or house kitchen. The structure must also be secured with locks on doors and windows to prevent breakins and theft of inventory or equipment.
Since alcohol is classified as highly flamable (explosive?) vapor (and alcohol flame is nearly invisible), your local fire marshal may be reluctant to sign off on a building or use permit if they are not familiar with fire safety requirements and practices for distilleries. The fire marshall is thinking of the safety of his staff should they be called out to your site in an emergency. The ADI forum can help in this area, too - they can offer up knowledgeable fire and other code inspectors for your local inspectors to talk to, which in many cases can help move things along. Having inspectors talk to each other usually works better than trying to educate the local inspector yourself.
The core members of ADI claim to be responsible for getting the American microbrewery movement started in the 1980's and 90's. They are now working towards starting a microdistillery / artisan distillery movement in much the same fashion. Though I have not begun distilling, I have found the information on ADI credible, educational and extremely valuable.
No, it is not legal anywhere in the United States to distill alcohol, unless you have a license. It is not practical for individuals to get licenses for beverage alcohol.
On a side note, I hear it is relatively easy to get a home-distillation license for producing ethanol fuel. It would be illegal for you to consume that fuel, and any of it that leaves your premises must be denatured (made unfit to drink). Fuel ethanol is most commonly denatured with gasoline, since most ethanol-burning vehicles consume a mixture of up to 85% ethanol, and 15% gasoline (this is the E-85 mixture). This is something I researched in great depth a few years ago, when gas prices started climbing, and I had a pickup truck that could run on E-85. Being in New England at the time, there was not a viable fermentable source that would make economic sense to make my own fuel, so I abandoned the idea, and bought a hybrid car instead. But, I digress....alternative fuels are not really on-topic for this site....
While you can't legally use a still for distilling your homebrew, you could 'freeze distill' it. Technically it's concentration, not distillation, but gives you a nice boost in ABV.