Conventional fan controls I've seen here use capacitor-start to start the motor and a simple potentiometer in the switchboard to control the voltage to the fan thereby changing it's speed.
The most ancient speed controls used an L-pad. Simple, fairly
low loss, and hard to find anymore.
Inductive loads can be controlled by triac / SCR dimmer styles
but there is more voltage applied at the current-zero-crossing
which the design has to accommodate (lamp dimmers have it
easy). This is really just component selection (but you need
to have the right goals).
There's a lot of stuff out there on "triac induction motor speed
control".