At the scene of the accident, be it a slip and fall, car accident, etc., take pictures to preserve evidence, write down the contact information for anyone involved and any witnesses, and get medical help. If you already left the scene, you may rely on the police report and other evidence to obtain this information.
If paramedics did not arrive at the scene of your accident or you did not go to an emergency room, be sure to see your doctor as soon as possible. The insurance adjuster may point to the amount of time between your accident and the start of your treatment to lower the value of your injuries. Start treatment for your injuries and then you can start on your claim.