1) Exchange Information
The first thing you need to do after a car accident is exchange insurance information with the other drivers involved.
2) Report the Accident
In the state of California, you are required by law to report any accident with more than $500 worth of damage. Minor accidents under $500 damage can be settled without reporting them and many times this is what people do. Most auto insurance policies these days have deductibles around $500, so many people would rather just pay for the damages out of pocket than risk higher insurance premiums.
If you are in an accident where there is over $500 damage, you will need to file a police report. This will help you later when the time comes for your insurance companies to assess fault.
3) Contact Your Insurance Agent
Whether you have State Farm, Gieco, AAA Insurance, Allstate or any other insurance provider, and regardless of who is at fault, the first thing to do after car accidents with more than $500 damage is to contact your personal insurance agent. They will help you start a claim if you are at fault, or go to bat for you with the other driver's insurance company if they are to blame.
4) Find a Quality Body Shop
Once you have talked to your agent, it's up to you to find a body shop that can repair your car to your satisfaction. The insurance company is obligated to pay the bill at whatever body shop you choose, so it is best to shop around for the best quality collision shop you can find.
The different insurance companies have different policies when it comes to recommending body shops. Body shop "steering" by insurance companies is illegal in the state of California, so insurance companies can recommend a body shop but they cannot require you to go to any shop in particular. Auto body shops that are recommended by your insurance company are called DRP shops, or "Direct Repair Program" shops.
These DRP program collision shops, for the most part, do good work. The only downside you might find is that with the high volume of cars they repair for the insurance companies, some of these body shops can have issues with repair quality.
The best way to make sure the auto body shop you choose consistently does great quality work, is to check the shop's 1-star reviews on Yelp or Google. Many times these low reviews deal with personality conflicts, but when a shop gets bad reviews for the quality of their paint matching or the use of cheap aftermarket parts instead of the manufacturers factory parts, that's a big red flag.