In order to gain U.S. citizenship after birth, in California or any other state, people may apply for derived citizenship or they may apply for naturalization. Derived citizenship is based on a parent already being a citizen. Naturalization is governed by the Immigration and Nationality Act.
The naturalization process begins with the filling out and filing of the Application for Naturalization, Form N-400. Sometime after the application is filed, the applicant is required to pass a naturalization test that covers ability with the English language and knowledge of U.S. civics.