I only did it once in America and this was some years ago so maybe it's changed... but basically you have to somehow pay in advance. How do you do that without knowing how much petrol you'll need? Very good question! If I recall I basically overpaid and they refunded me or something like that. Crazy.

As an American, I always put my card into the pump itself and then fill up. No guessing, no change, no even going inside for a normal visit.

One time I went inside to buy a can to fill up, and I also paid upfront for a gallon, which made the pump cut off automatically.

I've never tried to pay for an unknown amount of gas with cash, and never felt any need to.