You can find contact information and an address for each office online, as well as a website. They are listed alphabetically at https://www.dhcs.ca.gov/services/medi-cal/Pages/CountyOffices.aspx. Look on the website for more information about your local office. You can find office hours, as well as any information you may need to make an appointment. Make an appointment if the local office asks you to. Go to the closest office and ask for an application for Medi-Cal. They should have paper applications on hand, as well as people there to assist you with any help you may need. Add your main biographical information, including your name, Social Security Number, address, and phone number. You will also need to fill in basic medical information and details on income for you and every other dependent in your household. You will also need to fill in the information for your spouse if you're married. Date the application, as well. If someone at the office filled it in for you, you'll still need to sign it to show that you asked for that assistance. Wait 45 days for a reply in the mail.

Summary:
Find your local county office. Click on the website for your local office. Visit the office in person. Fill in the needed information. Sign and turn in the application.