Candidate qualifications and requirements depend on election type. In California, candidates must be:

A registered voter and otherwise qualified to vote for the office at the time that nomination papers are issued to the person or at the time of the person’s appointment. (Elections Code § 201)
Other rules depend on what cities and the California Constitution dictates.

The Candidate Handbook and Resource Guide provides information for the primary and general elections, such as candidate qualifications, filing procedures and calendar of events.