I have been told that my great-grandfather was a Mason in California, and that it is possible to request such records. I have no information on how to actually do that, and haven't had much success. How might I go about getting any such records?
There is a related question How to find out which Freemasons' lodge grandfather belonged to? which has some general resources.
You are likely to receive the same kind of information that is found on the Massachusetts, Mason Membership Cards, 1733-1990 database on Ancestry.com:
These cards contain last residence information, birth date and location, death date, the lodge an individual belonged to, date of membership, and occupation. Once you determine a local lodge affiliation, it may also be worthwhile to learn where their records are archived. Clues like dates of residency, birth and death dates, and offices held in the organization may be included in the lodge’s historical records.
If you don't have information about your great-grandfather's Mother Lodge in your historical records, see if you can find out from an obituary or newspaper article.
If you don't know your great-grandfather's Mother Lodge, the next place to try is the Grand Lodge of California. Unlike the Grand Lodge of Texas (from the linked question), there doesn't seem to be a link for Genealogy requests. The contact information is:
Grand Lodge of California
1111 California Street San Francisco, CA 94108 415/776-7000
The person who usually answers the genealogical inquires is the Membership Secretary.
Lodges, like many organizations, are set up to serve the needs of the present-day members. They generally don't have archivists who can pull a member's file and send you a copy, like getting a government record from NARA. But it is still worth asking -- the Membership Secretaries in Scotland confirmed the information I already had from the Massachusetts database and gave me residence information I didn't have yet (and were very cordial while answering my inept inquiries).