If you are at fault in an accident and cause property damage and/or bodily injury you should inform your insurance company that an accident occurred and give your description of how it happened. Your insurance company's claims department can then get the claim file started for the incident and be ready with a claim number when the other party calls in their claim for the damages they sustained.
If you have damage to your own vehicle that you are going to place a claim for under your collision coverage you would also make the claim when you call in to report the accident.
You can wait to see if the other party makes a claim against your liability coverages, but if they sustained damages they will normally do so within a few days of the accident. If you have not called in the accident by the time the other party calls your insurance provider's claim then your insurer will start the claim with the information the other driver has given and then contact you to find out if you are responsible and liable for the accident. They will do so by also getting your description of the accident.
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[Let CarInsurance.com help you find affordable auto insurance now.] To make the claims process easier you can contact your insurance company first and advise them of the situation. If you need to know specifics about how to place a claim with your insurance company or tell them of the possibility of a claim being filed by the other party, speak to your agent. You can also read the following articles in our Learning Center that deal with the claims process:
Simple Steps to Filing a Car Insurance Claim
Negotiating An Insurance Claim Settlement
Function of an Insurance Adjuster | 
