What should I say (or not say) at the scene of the accident?
Aside from exchanging insurance and contact information with the other driver(s), and speaking to them in the course of any absolutely necessary discussion, do not make statements to anybody at the scene of the accident except for the police. What you tell police officers at the scene of the accident can come back to bite you if and when you seek compensation for any damages you might have incurred as a result of the accident.
Do not admit fault. Whether or not you honestly believed the accident was your fault, do not admit fault to the other driver(s) or to the police officer. You do not have all of the facts yet, and prematurely claiming responsibility could prove harmful. Unbeknownst to you, the other driver might have been speeding or texting, etc., a traffic light might have been malfunctioning, etc. Any number of factors, which you are unaware of immediately after an accident, could have contributed to the accident.
Do not claim to be free from injury. Your back might feel fine at the scene of the accident, but it may start to cause you serious pain in a week. Some injuries do not appear until days, weeks or even months after the accident. Saying you are “fine” can complicate your ability to seek compensation for your injuries later.