How do I stop a dimmer switch from humming?
All dimmers buzz a little bit.  They "chop up" the AC waveform, which creates mechanical vibration (buzzing) and electrical noise (EMI).  Usually they are the most quiet when the lights are fully bright, and get louder as you dim the bulbs.  Here is a good page that describes what is happening.  A different dimmer may be quieter, although Leviton does make solid products.

I suspect, however, that you may be using the "new" CFL (compact-fluorescent) bulbs?  They're the ones with the twisted white glass tube.  The electronics in most of these bulbs interact poorly with the dimmers and can cause a lot of noise problems, both audible and electrical.

Now that it has become difficult to find incandescent bulbs (at least here in the USA), a lot of people are having to choose between paying substantially more money for "dimmable" CFL bulbs, or simply replacing their dimmers with simple on/off switches.

Good luck :)