I have been living in California for about ten years, but do not have any immigration papers. Is there a way for me to get a green card here? Where would I go to apply?
If you are living in California and are undocumented (or you have a temporary visa or status that will run out soon), the first thing to understand is that immigration law is federal. In other words, it mostly does not matter what U.S. state you live in--your prospects for obtaining lawful permanent residence in the U.S. (a green card) depend on the same set of immigration laws that applies across the whole country.
Unfortunately, as someone who has been living in the U.S. unlawfully, your chances of qualifying for a green card are slim--but worth looking into nonetheless. You should check with an experienced immigration attorney for a full personal analysis.
You may have heard rumors that ten years of living in the U.S. qualifies you for a green card, but those rumors are only partially true, as described in, Green Card Through Cancellation of Removal (Non-LPR): Who Qualifies?. Most importantly, you can apply for cancellation only if you have already been placed into immigration court proceedings. (Another possibility to look into: If you arrived in the U.S. while you were young, you might at least qualify for a temporary work permit under the DACA program.)
Of course, there is a chance that you will be arrested by U.S. immigration authorities who discover that you are living in California unlawfully and place you into court proceedings. For what happens after an arrest, see Nolo's articles on Noncitizens in Deportation or Removal Proceedings.
Unless you already have an order of deportation on your record, you should be given an opportunity to present your defenses to deportation--possibly including cancellation of removal--in front of an immigration judge. The immigration court offices in California are found in Adelanto, San Diego, El Centro, Imperial, Los Angeles, and San Francisco. See the EOIR Immigration Court Listing for more information.
One last thing to realize about living in California is that it's part of the Ninth Circuit group of federal courts. That means that if you had to appeal denials of your immigration case all the way to the federal court of appeals, the law developed within the Ninth Circuit would apply. This can actually cause differences in how a case is treated. For instance, different circuit courts sometimes take different views of the seriousness of a crime committed by an immigrant.
If you are not arrested, and happen to qualify for a green card, the first petition or application that you file (or that a family or employer files for you, as your petitioner or sponsor) will probably be by mail. It might not even be to an office in California.
As a later step in your application, you would, however, probably need to visit an office of U.S. Citizenship and Immigration Services (USCIS) for an in-person interview. USCIS offices that serve the public--usually called "Field Offices"--can be found in Fresno, Imperial, Los Angeles, Sacramento, San Bernardino, San Diego, San Fernando, San Francisco, San Jose, and Santa Ana. See the USCIS Field Offices list for more information.