What mechanism controls a ceiling fan speed?
They are generally controlled by switching between 3 different in-series capacitances. Full power is shorted/0F. The other two appear to add reactance to the circuit in series which is an a/c resistance at 60Hz thereby lowering the power reaching the fan.

I've seen mention that another way would be to select between the number of coils on the fan motor itself, but I'm not sure how prevalent it would be.

Also review the top answer here for some more background.