An apostille is a government certification that authenticates documents for legal purposes in other countries. Think of it like an international notarization. Just like a notarization, the apostille authenticates the signature and capacity of the official that signed it, but not the contents of the document.
The apostille is defined by the Hague Convention of 5 October 1961 Abolishing the Requirement of Legalisation for Foreign Public Documents. The HCCH provides templates in several languages, but the California apostille is bit different, see below.
The California Secretary of State (SOS) authenticates signatures on documents issued in California and signed by a notary public, county clerk, superior court clerk, and certain other government officials.
Apostilles are issued out of the SOS offices in Sacramento and Los Angeles. If you need an apostille, make sure to find out if you need it for the original document or the translation! If you need an apostille for my translation, I'll have my signature on the Translator Certification notarized. You then mail it to the California Secretary of State in Sacramento or take it in person to the SOS office in Sacramento or LA.
See details and application procedure on the SOS website.