Car accidents--even minor fender benders--can be very upsetting. But remember that anything you say can and will be used against you in a court of law.
If you are involved in a car accident with passengers in your car, you should first make sure that you and the passengers are physically okay. If there is any question as to whether anyone is hurt, call 9-1-1 immediately. The shock of a car accident is likely causing an adrenaline rush in everyone. Those hormones may be masking serious pain. So, if you see anything that sends up a red flag, take the safer approach, and call for a paramedic. If the other driver comes up to your while you are accessing injuries or calling for help, simply say to the driver "Hold on! I'm calling 9-1-1." It is completely fair to otherwise ignore the other driver when calling for help. If the other driver is standing next to you saying things like "no, I need your driver's license right now" or "we don't need paramedics" just ignore them. Your first priority is safety.
Assuming everyone in your car is alright, you will need to address the other driver. Again, safety is your top priority. Get out of your car calmly. Do not yell. Do not apologize. The first words out of your mouth are "Is everyone in your car alright?" If not, call for help immediately.
If everyone in both cars is alright, the next words out of your mouth are "I'm going to take a quick picture of your license plate and then let's pull into that nearby [gas station/ rest stop/ grocery store/ whatever.]" If the other person says "You can't take a picture of my license plate" you don't need to respond. Just take the picture and again suggest moving out of the way of traffic.
Once you both are out of the way, you can go ahead and call a parent or friend who can help you and calm you down if you would like. Otherwise, make sure you take pictures of your car and the other car. Take pictures of the driver's license of the other driver. Do not EVER apologize at the scene and do not lose your temper.