What does your car insurance company do for you?

If you are not at fault in an accident, what will your insurance company do in order to get your car fixed? How much help will they give you, or are we supposed to settle everything, make the calls etc. with the other carriers insurance. I was hit from behind while I was stopped at a yield sign. The other drivers fault ( a no-brainer). Yet I am getting different information from my agent, the other drivers agent, and even the auto-repair shop !!! Any feedback will help greatly.