If you've ever taken the time to look at the back of your insurance card, you'll see that the first tip most, if not all, insurance companies give you in the event of a car accident is "Do not admit fault." Some insurance companies use the word "never." This is absolutely crucial as anything you say can and will most likely be used against you. Do not ever admit fault. Even if it is your fault, do not come out and say it. Key phrases to avoid are, "I'm sorry," "I didn't see you there," and "I didn't mean to..." You should absolutely check to make sure no one is injured but do not apologize for the accident even if you think it was your fault. Oftentimes, it's not.
Provide just the facts to the police officer who arrives on the scene. Stick to the facts and avoid giving any specific details. Ask the police officer who investigates the traffic scene to provide you with a business card and with the incident number, so that you can obtain an accident report. Most officers will provide this information to you, even if you don't ask.
Call your own insurance company and report the car accident immediately. Your auto liability insurance policy requires that you do this. Just as you did with the officers on the scene, provide only the facts of the accident to the insurance company representative. This includes the date, time, and location of the accident along with the names and addresses of all parties involved. Avoid going in depth and giving details about how or why you think the accident occurred. This is not to say that you should lie to your insurance company. That would be fraud. Just stick to the facts. Do not give a recorded statement, even to your own insurance company, as it is important to understand that you should consult an auto accident attorney before discussing anything related to "fault." An experienced attorney will take control of the case and the release of information.
Accidents are never an enjoyable experience. It's easy to get overwhelmed and hyper-excited in such situations. Regardless, what you say and what you do immediately after an accident will impact your claim and your premium.