Firs of all, u don't need to talk to other insurance company. You would inform ur insrance company, proivde them all information including the other person's info and insurace, the persons from ur insurance company will come and look at ur car whether to repair or to salvage it based on damages. They will take care of any repair work needed, you do not need to pay (deductible you shud pay depending on the insurace).

It's ur insurance company duty to contact the other insurance and redeem the money they spend on your car and on you. So firs of all contact ur insurance, don't go after other insurace.