If dialup works over POTS just like a phone call, how was it possible for many people to dial the same number/connect to the same place at once? How didn't they get a busy tone?
Essentially because the dial up server has more than one POTS circuit associated with it. By contrast, a residential line has one circuit, so when A calls B who is on the phone, the circuit is already tied up. The dial up server would not have one phone line (circuit) but many, aggregated into an entity known as a trunk. Different size trunks are possible depending on anticipated traffic patterns. Of course, if you get it wrong, it's still possible for a trunk to fill up, and give you the busy signal.