California is a may issue state. Most states are shall issue conceal carry states.
Here in Missouri (a shall issue state) the sheriff collects a fee, finger prints you, does a back ground check with the FBI and will issue a permit if he/she feels you are ok. This is after you pass an approved cc gun class.
There is a time limit for the sheriff to say yes or no. If the sheriff says no, there is an appeal system in place for the citizen.
A map of the entire US showing how the various states handle concealed carry at
http://standeyo.com/News_Files/Firearms/right.to.carry.html
California,,,,, it all depends on the local sheriff is my understanding.