Tires screeching, glass breaking, and panic sets in, after all no one expects that an accident will happen to them, but the best thing to do is not panic and keep calm. It's very easy to keep calm, but if you keep a cool head then you can alleviate this stress as much as possible.
The most important thing to do first is to make sure everyone is ok. Check yourself and your passengers first. If at all possible check the other car also. Try to stay off the road to avoid another accident. Then you must call the police. This is very important, even if it is a small accident where nobody is hurt. You want to make sure everything is documented, and you get to tell your side of the story.
While you are waiting for the police to arrive you will want to assess the damage to your vehicle. This is a good time to get your cell phone out and take some photos of the damage. If the vehicles have not been moved, take some photos of the accident scene. This could help the insurance companies later determine fault and other questions. Go ahead and exchange information with all parties involved, in case you need to let the insurance company know any of this information. Call your insurance company as well so that you can file your report as soon as possible. Make sure to tell the complete truth, as you may be recorded.
If you can follow all these steps calmly, you should have no trouble filing the claim and getting the insurance company to pay the money you are deserved.