There are two different kinds of marriage licenses you may obtain: a standard license requires one or two witness signatures. The license may be obtained in any California county, and is valid for a wedding anywhere in California.
Unlike a standard license, this does not require any witness signatures. Also, the details of your marriage are not released to the public marriage record (some couples prefer this for privacy reasons). The one caveat of a confidential license is that the couple must state that they are living together (at the time the license is issued) and provide the same address.