How do I go about marrying my fiancé while he is in jail in California?

Have you called the jail and asked them? Try that first. You'll probably get someone there to help you such as the pastor of the jail.

Have him request a marriage packet and you both fill it out. Also have him talk with the Chaplain.

First how long does he have. Just one thing to consider.
But each jail has its own rules is this a "jail" or a "prison'

But the local instituion may have a plan o fix his