Exchange names and other relevant details with the other drivers and get details of any independent witnesses. If someone refuses to give you their details, your insurance company may be able to trace them through their vehicle plate number.
Tell your insurance company about the accident straight away, even if you do not want to make a claim.
Take photographs that you may be able to use later as evidence if you need to make a claim.
If you have third-party insurance:
You should make a claim against the other driver and allow the insurance company to decide who is responsible for the accident.