Clarification of speed control

D1 is a temperature sensor. Voltage drop developed over a diode will drift with the temperature. Usually silicon diodes have a negative temperature coefficient of -2mV/C.

R5 and Z1 make a 10V voltage regulator. As the temperature increases, voltage drop over diode D1 will decrease making voltage at the "+" input less than voltage at the "-" input, opamp will drive it's output low turning on the fan.

R3 accounts for varying current - when voltage drop over diode decreases, more current will flow thru it. By connecting diode and pot to common point at R3 designers make sure that this does not affect the temperature point set by a potentiometer.

R4 provides hysteresis - it affects the voltage at "-" input a bit so that the output will not oscillate at the specified temperature.

The circuit I believe you're looking for is something like this:
(please excuse the odd symbols for the switch & motor ...)

^{simulate this circuit – Schematic created using CircuitLab}

With the switch in the Low seting, only C1 is connected in the circuit.
When the switch is set to Medium or High, either C2 or C3 will be connected in parallel with C1, giving you a larger capacitance which (I believe ...) will produce a faster fan speed.
It would not be uncommon for the capacitance value for the Low speed setting to be low enough that the motor won't start spinning by itself.
Ceiling fan speed control switches are usually wired such that the switching sequence runs Off - High - medium - Low - Off, so that the fan starts up with the full-speed capacitance to get it going.
You'll probably need to do a bit of experimenting with capacitor values, but a rough guess would be to choose a full-speed total capacitance of about 10x the value which just barely allows it to start.