Who will the insurance pay?

We recently got into an accident, and contacted the other partys insurance to file a claim. Their insurance is Triple AAA. Today we got a call saying our claim was approved, the other party is not contesting that it was their fault. What does this mean? Do we find a place and get it done? Do they do it for us? If we get the check, what if the repairs cost more than what Triple AAA PAID US?