How do you "prove your belongings" to your insurance company when your house burns down?

I caught a piece of toast on fire last night and set off the smoke alarm, and it got me thinking about the fact that some freak accident like this could happen and we could lose our home. That thought lead to the worry that I don’t know how to prove what belongings were inside the house if it were to burn. We have our house insured for a definite dollar amount, and the belongings insured for another amount, but I’m pretty sure we’d have to show that we actually had that amount of valuables in the house to receive any money. If your house is gone, what do insurance companies want as proof?