Does this person I marry become an instant citizen or what right does this person have in California?
I assume that you are a US citizen. Your spouse would not automatically become a US citizen just because you get married. First s/he needs to get permanent residence (green card), and then s/he can apply for citizenship after a few years.
There are a couple of steps to permanent residence, and many forms to be completed. The process takes about 6-12 months, and varies by local office processing times.