Update: ThreePhaseEel and others thank you.
Is the T/P symbol on the motor schematic stands for Thermal Protection? Right below the schematic diagram of the motor in big letters it states Thermally Protected.
The external thermal protection is probably for knowing when the fan has to come on for microwave usage, because the microwave needs to cool and NOT for protection of the motor itself. So I think this thermal protection and one of the yellow wires going to this thermal protection can be eliminated if the unit is going to be used for a stand alone fan.
Just to clarify: So a double switch is needed if both speeds are to be used but if only high speed is going to be used then just the blue wire needs to be connected to power and it can be turned on/off by connecting and disconnecting the power cord.
For a double switch the blue wire from the motor to one side of switch for high speed and yellow wire to the other side of the switch for low speed. The other side of the switch gets the black wire from the 3 prong plug.
The black wire from the motor is connected to the white/neutral wire from the 3 prong plug to complete the circuit.
What about the green wire of the 3 prong plug? Where does that goes or is it left out?
The capacitor stays for the initial motor torque. Nothing to do there except to enclose it in the same box as the switch and to insulate the wires going to it