Auto insurance is great to have (and in the state of California, mandatory as well). You can go around without worrying that your car will be stolen or that you’ll go in debt in case of an accident.
However, no auto insurance will protect you from actually having the accident. That’s your responsibility. It’s not that hard; respect the speed limits (they exist for a reason), don’t drink and drive, and don’t drive if you’re too tired, among other things.
Nevertheless, when an actual accident happens, it can be a very stressful and frightening situation, especially if someone is hurt.
First of all, stay calm. I know that staying calm is hard to do in a car accident, particularly if someone (for example, you) is bleeding, but you must. Otherwise you’ll probably make things worse. By staying calm, you will be able to make better decisions.
Make sure that you’re alright and able to walk and talk properly. If someone is hurt, call the paramedics immediately. Then call the police. Try to get the local police as each jurisdiction will have its own way of dealing with accident reports.
Then, try to gather as much information as you can. You need plate numbers of each car involved, the names of every driver and vehicle occupant and their phone numbers. The names of any witnesses and their phone number as well. This is why it’s a good idea to carry a small notebook and a pen in the glove compartment. It’s also a good idea to have the numbers of the police departments of the areas where you drive most of the time (for example, home and work, if they are in different ones).
You will then have to report a claim with your insurance company. You have to provide all proof and information of the accident (which is why a police report is so important). Gather all the documents that you can, like hospital bills, pictures taken with your cell phone, etc. By law, the insurance company will have 15 days to acknowledge your claim and 40 days thereafter to conduct an investigation and accept your claim in whole, in part, or deny it. Afterwards, it has 30 days to pay you back.
Anyway, even with auto insurance, the best thing to do is to drive safely and avoid accidents. Also, keep one copy of your insurance policy in your car, one in your wallet (or at least the company’s phone), and one in your house. It’s always better to be prepared.