Speed control of single phase induction motors can be achieved by driving them at different frequencies - more complex and expensive than is usually appropriate, or by changing drive to the main winding or start winding.
Many examples and discussions are available on web.
Driving whole motor:
Microcontroller driving while motor with TRIACs.
Freescale An3471 - Ceiling Fan Speed Control - Single-Phase Motor Speed Control Using MC9RS08KA
Relatively simple. I'm somewhat surprised that they say you can achieve good results this simply. Freescale SHOULD know what they are doing.
Need not use a microcontroller.
Here U1 is an optical controlled TRIAC which is used to trigger the larger TRIAC Q1.
Shaded pole motor control with PIC - You tube
Separate out windings:
New method for speed control of single phase induction motor with improved motor performance
Abstract only but very useful.
Diagram thumbnails small but useful.
In this paper, a new method of speed control for the single phase induction motor is introduced to overcome the disadvantages of the conventional methods. In this method, the magnitude of the main winding current and its angle are controlled to control the motor speed, as well as to increase the starting torque at all speed settings. In the meanwhile, the voltage applied to the auxiliary winding is kept constant at the rated value. The performance of a 1 hp capacitor run single phase induction motor is experimentally and theoretically investigated, using this method of speed control. The experimental rig is built in the laboratory and a complete set of test results is obtained. On the other hand, a mathematical model for the motor is developed and the motor performance is calculated. Good agreement between the experimental and theoretical results is obtained. These results show that the new method of speed control gives much higher starting torque. This enables the motor to start at low speed settings. Also, a great improvement in motor efficiency and power factor at all speeds is achieved.
3 methods - diagrams dead
[Microchip AN984 - An introduction to AC Induction Motor Control using the dsPIC30F MCU]