No need for any laughing! An honest question deserves an honest answer.
As you already know the center screw on the Atlas switch machine is a ‘common’ terminal. The other two are the ‘switched’ wires to energize one coil or the other on the machine.
Your ‘other’ side of the circuit would go to the center terminal of the single-pole, double throw electrical switch.
If you sketch out the wiring you’ll have a better visual understanding of how it works.
There’s a little discussion about the Atlas switch machine wiring here:
Good Luck, Ed