The principle is simple on purpose. For every day of medically necessary inpatient treatment, the insurer pays the agreed rate, from the day of admission to the day of discharge. There are no receipts, no billing with the hospital and no offsetting against other benefits. You can insure the component either as part of a full-cover plan or as separate supplementary insurance, which people with statutory health insurance can also take out.
You choose the amount when you take out the policy. Usual amounts are €20 to €100 per day. Because the premium rises with the daily rate, it is worth asking honestly which incidental costs a stay realistically creates. All amounts are guide values. What counts is the plan.