Thankfully no signatures involved. You roll up, swipe/dip/tap your card in a reader on the gas pump, enter your postal code (archaic security measure from the pre-chip card era), wait a few moments for the electronic authorization (they pre-authorize an amount in the $75-150 range), then pump, and leave.

If you are paying cash, you generally have to go inside before pumping and prepay, and then go back inside afterwards to get your change, if applicable.

That used to be typical in the US as well. I think that when pay-at-the-pump became the norm (using a card), prepayment became expected even when paying with cash inside, at around the same time. I expect there are some gas stations here and there in the US that still operate the way you describe though.

An increasing number of gas stations are completely unattended though — the attached store might close overnight but the pumps are still usable.

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.