What's the cheapest/fastest way to put a potentiometer on an ac fan?
If you mean that you want to control the speed of an AC fan with a potentiometer,
 it is probably not possible. 

Whether an AC "mains" fan can be speed controlled with a pot depends on the technology used.
 Motor type is liable to be 


"shaded pole" induction motor. Smaller fans used in appliances, fan heaters, pedestal fans etc.  (All typical older type small fans and many new ones) 
Single phase induction motor - capacitor start usually. Larger fans.
Brushless DC motor (newer but less common even now due to high voltages involved). 
Series wound "universal" motor.
Possibly other. eg brush motor. 


A brush motor may have permanent magnets and would then be a DC motor and would be unlikely to be found in an AC mains fan application. 

A brush motor with a wound rotor may be
- Parallel wound - unusual - speed control possible but not without motor modification.
 - Series wound - see below.  

ONLY the universal / series wound motor is suitable for speed control with a series resistor. All other types will not be able to be properly speed controlled with a series resistor and may be damaged. Speed MAY be slightly affected by a resistor but the end result will not be predictable or consistent or safely useful. 



Speed Control:

The speed of "Induction motors" is based on the AC mains frequency. They "slip" slightly relative to the 50 Hz waveform. Altering mains frequncy is the only way to control speed.

Brushless DC motors can be speed controlled using an appropriate electronic controller. A version of this will already be built into the motor BUT is liable to be a "go as fast as you can" type and is unlikely to be able to be accessed or modified.

Series wound universal motors can be operated on DC or AC and speed is related to applied voltage (not necessarily linearly. Unloaded they will spin up to very high speeds and may self-destruct. Vacuum cleaners often use series wound motors and their motors would be a suitable candidate for speed control. A series resistor for controlling speed would need to be able to handle power levels of the same level as the motor itself.