How do you make an insurance claim when someone hits you if you dont have insurance and they do?

You don't need to have insurance to collect on an insurance policy. Just call their claims department and they will get it started.

The only issue is that in some states, such as New York, insurance is mandatory in order to register an automobile and be able to drive it. If you are in such a state, and you file a claim for an accident in which you did not have insurance, you could well be charged for driving without insurance and you would probably lose your license.