What are the steps to take when you saw someone hit your car with their door in a parking lot Is their insurance going to pay for this do you have to get your insurance involved?

The first thing you should have done was call the police so that you'd have a report to submit to your insurance proving someone else was At Fault. Barring that, you can still submit a claim to your insurance. If you know who damaged the car, you can settle it without insurance, but it's not recommended. People often agree to pay for damages until they get the final bill, which is always more than they expect. Then you'd have to sue them for the money in civil court. The other option is to simply have the damaged fixed and pay for it. But your best bet is to submit a claim to your insurance, who will go after the person who damaged your car, assuming they can track him or her down.