Go to DMV, ask them for a DL 51 with the green medical exam card attached, get the same form you use to get a California ID or California Driver License, their LiveScan form, and pay $5 for their blue ambulance driver handbook.
Go to a clinic, have them do a medical exam using the DL 51. I hear most places are around $80. At the end, they should give you a filled out green medical exam card and the DL 51 form. The green medical exam card you keep in your wallet and you must have it on you when driving an ambulance. The actual form you give back to DMV.
Google "LiveScan (name of city you live in)" to find a place nearby that does LiveScans. Some places business are dedicated only to LiveScans, others may be like UPS or security related (e.g. county sheriff office). Find out if you need to bring more than just a picture ID and bring the LiveScan form DMV gave to you. This information will automatically be sent to DMV afterwards and you won't have to worry about it. This may also cost around $80.
Study the blue ambulance driver handbook. AMR used to have the test questions, but it seems that website doesn't work anymore. There was a discussion on that
here and somebody shared an alternative link that shows the test questions still, but without answers unfortunately.
Fill out the form they use for California ID or California Driver License, but instead check off "ambulance driver certificate" on it.
DMV will probably be more confused about it than you are. Be patient. Work with them.
They'll give you a temporary cert on the spot (pink one) that expires after 180 days. They will mail you the actual cert within the 180 days, or you you'll need to go back and find out what went wrong/why you didn't get it. You must keep the temporary or actual cert on you with your green medical examiner card while driving an ambulance. In my area, companies won't hire you unless you have the actual ambulance driver certificate (not the temporary). If you do not have a ambulance driver certificate and green medical exam card, they can still hire you, but not for driving; you can only tech/be an attendant on calls. This is usually why ambulance companies do not hire people who not have both.
Like Firefite said, it's on the laws of driving and driving an ambulance. You will not drive any sort of vehicle to obtain your ambulance driver certificate (or people say ambulance driver license).
When you get hired, a lot of companies like to put their employees through a thing called emergency vehicle operation course (EVOC, or you might here CEVO too). A lot of EVOC has to do with driving the ambulance normally (without red lights and sirens). Companies may have their own system and rules on driving e.g. even though the law says we can drive 15 mph above the speed limit while driving with red lights and sirens (CODE 3), I heard AMR had their employees go no more than 10 mph. At another company, they are not allowed to drive CODE 3 on freeways. They may not allow you to drive for the first few weeks, and may not allow you to drive CODE 3 for the first few months. Some companies might just throw you on an ambulance without any training. It's up to the company.