What's the process to become a general contractor?

Every state is different. I see you are in Fresno, CA. Most states require you have a minimum 4 out of the last 7 years experience working for another contractor as well as be able to pass a state & safety test. Here is a good place to start.

http://www.cslb.ca.gov/

It probably varies from state to state.
In California, you have to take two tests:

  1. LAW
    2 TRADE