Stay calm as best you can. This is a bad situation, but you can get through it.
If you or someone in the car is seriously hurt--call 911 right away. If someone has been badly injured they should be transported to the hospital immediately for emergency care. If it does not seem that emergency care is required, still you should call the police so that they can make a traffic incident report. The report will help so that all the information is gathered, the witnesses are documented and you will have the opportunity to document any physical complaints that you may have at the scene.
If a traffic incident report is not going to be made then you will have to gather the information yourself. Do not admit fault ever; resist the temptation to apologize.
Gather as much information as possible, but you will certainly need the following:
Driver's personal information--name, phone # and Driver's license #. Driver's insurance information--insurance company's name, policy holder's name and policy number. Check that the policy is valid and matches the car and driver. Write this information down yourself; don't trust that the other driver will write down the information honestly.
Take pictures of your car and any other cars in the accident. Take a picture of the other driver. Take a picture of any skid marks, broken glass or other physical evidence. Remember, too much information is always better than not enough.
When you get home make a binder or folder to keep all your things and documents related to the accident. Stay organized.
Get treated immediately. You probably are not a doctor, so do not self-diagnose. You have just been though something stressful and traumatic, your body will respond with increased adrenalin, so you might not feel the symptoms right away. Go to the ER, urgent care, chiropractor or family doctor. The insurance company will argue that if you did not seek immediate treatment you were not injured, don't give them a chance to make this argument.
Once you have begun treatment do not got more than a few days between appointments. Avoid gaps in treatment of more than a few days.
OPENING YOUR CLAIM
Call and file a claim with your car insurance and the other driver's insurance. Ask your insurance if you have medical payments coverage. This is a no-fault coverage that can be used to pay for treatment related to the accident. This is particularly helpful if you do not have medical insurance. Do NOT tell the insurance company about your injuries or lack thereof.
You may get a call from either your insurance or the other driver's insurance within a few days. The adjusters ofter call very quickly so that they can get a statement about your injuries before said injuries have made themselves manifest; it often takes as long as a week or more before your injuries are clear. Do NOT give a statement about your injuries. Again, you're not a doctor. You can, and should tell them how the accident happened, but nothing else. You control the flow of information, not them.
FINDING A PERSONAL INJURY LAWYER
Find a local, reputable personal injury lawyer. I find a personal injury lawyer that exclusively does personal injury law. If a lawyer is truly good at personal injury they will have more than enough work to do only that. There are many lawyers that do other things, but will take a personal injury case if it comes their way---avoid this scenario. Your lawyer should be a personal injury specialist, not a jack of all trades.
You want a local attorney. Many law firms have local numbers that they put in yellow pages, but they are do not have a physical office in your area; this is not the same as having a truly local attorney that understands the area and the courts.
Check out their website and physical office, you can learn a great deal that way. Search the State Bar website or Avvo.com and make sure that they have not been disciplined; you want an ethical attorney.
Find one you like and call to set up a free consultation. Good luck!