I don't know your specific fan or switch.
Following link is TYPICAL illustration of 3-wire fan switch wiring:
http://waterheatertimer.org/images/Fan-motor-1-500.jpgThree way switch is designed to match TYPICAL fan motor windings.
Motor windings are insulated copper wire wrapped around metal fan housing, similar to electromagnet you can make by wrapping wire around a nail.
Inside the fan motor are two windings.
Winding 1 for low speed.
Winding 2 for medium speed.
And when both windings are combined, that makes high speed.
You have to test your switch.
Usually the hot lead connects to red. So the red connects to each of the other wires.
Then pull the chain and use continuity tester between red wire and other wires to see how the switch is set up.
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