Speed Controllers - How do they work?

I'm trying to figure out how these speed controllers actually control the speed of a turntable. I have a Clearaudio Champion 2, and the motor has a single AC power cord coming out of it. If I plug the motor into the speed controller, how does the signal to control the actual speed get to the motor to slow down or speed up the table? Maybe I'm missing something here, but I'm confused about how they work. I'd consider purchasing one if they are really worth having. Can someone explain this to me?
Speed controllers keep your turntable spinning at exact speeds. Once you own one you shall never want to be without it.
Hello Spenceroo,
Generally they vary the frequency of the electricity, not the voltage, to slow, or speed up the Motor Here in US that frequency is 60hz, in Eu it is 50hz.

Some speed controllers, such as the VPI SDS also ramp down voltage to a pre-determined setting after initial motor start up at full voltage. This is said as well to reduce motor noise with the lower voltage, thus helping lower the noise floor with it.
For AC motor, controller varies frequency. For DC motor, controller varies output voltage. Make sure you buy the right kind.
They also clean up the electricity going into the motor and back out through the AC to the other components.
So if I plug my Clearaudio motor into a Clearaudio syncro, the syncro is going to regulate the power to the motor to either slow down or speed up the motor? It reduces or increases the amount of electricity the motor receives? The less power to the motor, the slower it turns the platter and visa versa?

Sidssp already answered your question.

Power (wattage) has nothing to do with it.