Polyphase AC induction motors work by creating an rotating magnetic field. Creating a rotating magnetic field requires phase-shifted sinusoidal currents. For instance, two that are shifted by ninety degrees (called a quadrature), or three phase.
Single phase motors either use a nonrotating magnetic field (one that pulsates), or else they generate two-phase power internally with the help of a capacitor. Some designs just use capacitors for starting, or a large capacitance for starting, and a smaller one for running. You can see these capacitors: they are the one or two "cans" attached to the sides of a motor.
This page on All About Circuits has notes about single-phase motors: http://www.allaboutcircuits.com/vol_2/chpt_13/9.html
This page introduces AC induction motors:
This is the top page for motor topics: http://www.allaboutcircuits.com/vol_2/chpt_13/1.html
Regarding speed, induction motors develop power through lag between the rotating armature and the rotating magnetic field set up by the stator coils. If the armature rotates at the same speed as the magnetic field, that is called "synchronous speed". A deviation from that speed is called "slip". A motor runs at close to synchronous speed when it is unloaded and does not perform work. When a load is put on it, its speed slips and that causes it to deliver power. The power rises with increasing slip up to a point, and then it drops off. If you block a vacuum cleaner hose, you can hear the motor speed up. The reason for that is that the motor is actually working less hard (not moving air), and so it increases toward synchronous speed.
Controlling the speed of this type of motor is a tricky business because the synchronous speed is related to the frequency of the power line.
A triac-based light dimmer doesn't change the frequency. You may have some success regulating speed with a dimmer but it's not going to be very accurate. Basically it will choke off current to the motor, which will cause it to slip more under the same load.