Should I put a dimmer switch on a ceiling fan?
Check the fine print
To find out if the dimmer can work with the fan, you'll have to inspect the dimmer.  For this, you'll have to remove the cover plate and possibly pull the switch out of the box (in which case, make sure you shut off the power at the breaker). If you see the text &quot;For Incandescent Only&quot;; or something similar, you should not use this dimmer with a motor load.

Using a standard dimmer with a ceiling fan can damage the motor, and/or cause the dimmer and/or motor to overheat and cause a fire.
There are a few better options available to you.
Install a fan control switch
There are many different fan control switches available; with a wide range of styles and functions, you should have no problem finding just what you want. A simple control like this 3 speed fan control, will run you about 20 bucks, and installs using the existing wiring.

Install a remote control
If you're up for a bit more wiring, there are universal remote control kits available.  You'll have to wire the receiver into the fan housing, so it's a bit more complicated than installing the wall control. But once the receiver is installed, you can place the wireless remote anywhere you like. There are a ton of these things available, so you shouldn't have any trouble finding one you like.  You can even get a cool touch screen control, if that's what suits your fancy.

Install a new fan
If installing a new fan is an option, you could simply select one that comes with a remote control.