I know there were details posted on other forums in the past, so searching Google might be your best friend.
1 club is on the base. Active/retired military or contractors working on base are eligible to hunt. Details are here.
The other club is private and I believe is an equity ownership club. It is called the Ventura County Game Preserve. There is a large list of celebrities who are and were members at that club. John Wayne was one of them. This is a pretty high dollar club, at least for So Cal. Last I heard the waitlist is extensive.
In terms of other private fields/ponds... knock on doors.