Detail how the accident occurred, the injuries or damages you’ve sustained and (if applicable) the dollar amount you are claiming. Gather relevant records related to the car accident, be they medical bills, repair estimates, or police reports. Give the insurance adjuster all the reasons in the world to pay out on your claim. You may wish to retain an attorney to assist you with making the claim if you are uncomfortable doing it yourself, or if things get particularly contentious.
Comprehensive car insurance covers damages from an "act of God," or events that are not caused by a car driving into something else. An "act of God" can include things like damage from a heavy tree branch falling on your car. Since you have no control over when or why a tree branch would fall on your car, this kind of accident would be covered under your comprehensive policy.
Comprehensive insurance is commonly confused with collision. They both insure your car but cover different events. Collision covers car accidents, and comprehensive covers events out of your control. Think of it like this: Collision is colliding with something else (other than animals). Comprehensive is basically all other events. Accidents with animals are covered by comprehensive (and not collision) because these accidents are considered out of your control.