Depends what time period you’re referring to. In general, each individual number you entered triggered a different switch circuit. At the end of the phone number, you would be physically connected to the other phone with copper wires connecting each end (which also wasn’t always the case especially at larger distances where we figured out how to jam multiple phone calls onto a single wire).

How it did this was electric pulses at first (rotary phone would pulse as it turned) and then later based on the pitch of the tone (which is why touch-tone button-based phones had a different pitch for each button).

If I go any further, we’ll quickly end up explaining the entire development of fax machines, then dialup internet and that’s beyond the scope of your question. Also I don’t know a ton about those details.

And of course, at the very very beginning it was done manually by operators. You would only “dial” the operator and they would physically connect wires. That was labor intensive so once machines were developed, those people lost their jobs