First of all: get to a hospital and take all your legal documents with you. Make sure to have your passport and if you have it: your travel insurance card.
Then, make sure to let the doctor or nurse know about your insurance policy. The sooner they can connect you to your policy, the better.
In some cases, you’ll have to pay the cost of everything out of your pocket before filling in a claim. Make sure to have a decent travel card to pay for everything you need.
In other cases, your insurance company will take care of everything. Depending on the policy you have or the company you’re with, they will have guidelines to follow.
But always: the patient or victim needs to get help first. Payments and insurance come later.
Take pictures of all receipts you have during the time in and around the hospital. Those are not only hospital ills, but also bills for meals, drinks, transportation, and of course medical bills. Quite a few insurance providers will reimburse expenses you make at the hospital.