Here are the California regulations for marriage:

http://www.cdph.ca.gov/certlic/birthdeathmar/pages/marriagelicenseinformation.aspx

These regs. apply to every county in California.

Do you require an officially "ordained" minister or another person licensed in the State of California to officiate at marriages?

Depending on who agrees to do this for you, if they are ordained Christian clergy, they might ask if you are gay or straight. Many Christian clergy will not perform a marriage ceremony for gay people. It probably doesn't matter one way or the other for a non-clergy officiate.

You need to understand that the Christian view of marriage is that the couple marry themselves, the officiate is there as the witness for their church and/or the State. A priest or minister can explain this more thoroughly for you.

You might google the yellow pages for local Inyo County churches and contact those clergy directly: Lone Pine, Big Pine, Bishop, or Mammoth Lakes.