Get an estimate and repairs
An insurance company may require you to take your car to an automotive repair shop and get an estimate for how much it will cost to fix any problems that resulted from the fender bender. Some insurance companies may require two separate estimates from two different repair shops.
If you've received your estimates from businesses in your insurance company's network of authorized repair shops, your insurance company should approve the repair and usually will pay the shop directly. If you've already paid the repair shop out of your own pocket, and the insurance company deems you've paid a fair market rate, then it may send a check directly to you.
Hopefully you'll never have an accident and never have to use any of this advice. But if you do find yourself in a fender bender, at least now you'll be prepared.