Most of the time the car accident is going to be worked up by a law enforcement professional. What you should do is get a copy of the claim number or the case number and with that you’ll be able to obtain driver’s information, driver’s license information, and insurance information. Those are valuable items.
Also, that should also contain witness information. However, if you are able to at the scene and are not too severely injured, you should also find out witness names of people who have witnessed the accident. That’s extremely important.