Its not exactly what you are looking for but it will help link.

Its not exactly what you are looking for but it will help Arduino-controlled-light-dimmer-The-circuit.

Here is the sample project in which TRIAC is used with arduino for controlling the flow of current to the light. In your case Light or better we can say load is FAN. This will help you in controlling the FAN Speed. Relay only act as switch and it won't control FAN Speed.