No offense to jasonck08, but with the exception of car batteries not liking to be discharge very much, which is true, most of the rest of the post is not accurate.
It is a common misnomer that hours of sunlight = hours of solar energy. That would only be true under perfect conditions and with perfect tracking of the solar panel with the sun. Realistically you will not have perfectly clear skies and you are likely going to have a stationary panel. Hopefully you will not have any shade. If you do, that changes everything!
40 amp hours on a 12V battery with some charging losses (higher losses at the top of the capacity and need to overcharge a bit), so count on needing about 530 - 550 watt hours or at least 45 amp hours.
You are in California so I assume camping close. You are inland, so fairly clear skies, but lets be cautious and say 4 peak sun hours/day. You may have a great week, clear skies, and no shade and get 8/day, but then again you may not so be cautious.
You are likely going to have a PWM controller so at best extracting about 70% of what will come out of the panel.
I would say at least a 30 watt panel. If you can get bigger, you are more likely to have your battery near peak capacity which lead acid batteries like.
In terms of a controller, get a Morningstar Sunsaver10 or other high quality unit. There are dirt cheap ones out there, but do you really want to use a $20 controller with a $100-$200 battery?
Semiman