I binged CuriousMarc’s YouTube series on teletype restoration a few months ago, so here’s a simplified (and possibly somewhat inaccurate) explanation of how one works.
The only electrical components in a Teletype are (a) a continuously-running electric motor, and (b) an electromagnet and a few switches. Everything else is completely mechanical.
The Teletypes in a circuit, and the electromagnet and switches within them, are all connected in series, forming a current loop. (Current, rather than voltage, is used because you can use a constant-current power supply to get the same power at each electromagnet regardless of how many are in the circuit and how many miles of wire are between them.)
When the circuit is idle, current is flowing. This allows any Teletype to begin transmitting; if it were the other way around, each one would need its own individual line power supply. (Incidentally, this is the origins of the “break” key still found on many modern keyboards: when the circuit was disconnected, nobody could transmit, so “breaking in” to the circuit was how you interrupted somebody, and a lot of early computers used this as a primitive version of ^C.)
When you press a key, a rod is lifted, activating a clutch that connects the motor to the rest of the machine, which starts running. The first thing this does is break the circuit, deactivating the electromagnets in the receiving mechanisms of all the other Teletypes. When this electromagnet deactivates, it trips the clutch in those machines, starting them running so they can receive the character. (This is why it’s called the “start bit.”)
One-tenth of the way through the rotation, a cam in the sending machine switches from the “start bit” to the switch for the first data bit. If the rod on the key you pressed has a bump on it in the right spot, it will press this switch and send a “mark”; if it’s missing the bump you’ll get a “space” instead. On the receiving end, a clever mechanism connects the electromagnet to a lever: if the magnet engages, it pushes the lever one way; and if it doesn’t, the lever stays pushed the other way.
At two-tenths of the rotation, the first data bit switch is disconnected and the second data bit switch engages. This of course reads the second bump on the rod, and at the receiving end the clever mechanism has moved so the magnet pushes (or doesn’t) the second lever.
(Notable exceptions: the ‘ctrl’ key forces the first two bits low—this is why e.g. Ctrl+D and “End of Transmission” are the same—and ‘shift’ forces the first bit high.)
At three-tenths of the rotation, of course, the third bit is read, transmitted and received; this process continues for the remaining data bits.
The final two-tenths of the rotation are known as the “stop bits”, and consist of some signal that doesn’t matter much. The receiving end uses this time to trip the print mechanism: the levers that were pushed-or-not during the data bits engage with some bumps in some other rods, blocking all but one of them that matches the specific pattern, and then a thingie shoves forward, slamming the appropriate type bar up into the ribbon and paper, and as it returns the carriage advances one character. (The reason for using two bits is simply to give some time for all of this to happen.)
Finally, the mechanisms on the sending and receiving ends complete their full rotation, disengaging the clutch and coming to an abrupt halt; the transmitting end reconnects the line so the circuit is available, and everything is ready for the next character. All of this has happened in less than a tenth of a second, a mechanical ballet choreographed too fast for the human eye to see, and transmitting information potentially hundreds of miles at the speed of light.