Does installing dimmer switches on lighting reduce the amount of electricity needed to power the lights or is it just turned to heat at the dimmer
Modern dimmer use a circuit that chops the AC into shorter pulses. Shorter pulses with longer intervals between them don’t supply enough power for the bulbs incadescant bulbs filament to reach full operating temperature. So the bulb is dimmer. by changing the width of the “on” pulse, the lamps brightness can be controlled.
There is some small loss in the dimmer circuit, but not too much. So the dimmer is not converting all that power to heat.
Note that some dimmers can be used with florescent lights, but most cannot.
It reduces the total energy flow.
However, something else is important . Light bulbs are extremely inefficient. Most of the light that they emit is invisible. When you dim a light bulb just a little, you also shift the spectrum. This mostly dims the visible light but without changing the invisible light by much, so in that case the room gets darker but you’re not saving much energy.
It’s better to use a bunch of halogen floods on separate circuits, then turn them off one by one to dim the room. Halogen bulbs run at much higher temperatures than standard bulbs, so most of their light is visible rather than IR. (They even put out some considerable ultraviolet!)
Switching to compact fluorescent bulbs would save much more energy than incandescent on a dimmer or halogen. They don’t burn super-hot like halogen and their color balance is pretty close to incandescent these days. They come in many wattages (is that a word?) and fit in regular light fixtures. The only downside: they’re expensive. It takes years for the money saved from using less energy to equal the purchase cost. 
Dimmer controllers are usually “phase-fired proportional controllers”; they reduce the RMS voltage (and thus the average power) going to an incandescent light by switching off a triac (or back-to-back SCRs) somewhere in the 60Hz cycle. The triac/SCR’s do burn up some energy, but usually not much. And Bill is correct; incandescent bulbs put out a lot more heat (i.e. IR energy) than visible light, and reducing the brightness/temperature tends to also shift the spectrum in a way that doesn’t work in your favor. But to answer the OP – reducing the brightness is not a “zero-sums” game, i.e. it is not the case in that “the power that would have gone to the bulbs is now being burned up in the dimmer switch”; dimming the lights does save energy.
We have 2 dimmers in our house. They annoy me however, cos they make a buzzing noise. Can you get ones that dont buzz cos it really does my head in.
An excellent page on DBS (Dimmer Buzz Syndrome):
And as long as both dimmers and halogen bulbs have been mentioned, I’ll mention something about using the two together. That is, putting a dimmer switch on a halogen light ( a lot of those stand-up torchiere lamps have them ). Regardless of how the dimming is done, it’s a bad idea to run a halogen at less than full temperature all the time.
The halogens will only do a good job bonding with the filament material if the temperature is high enough, and if they don’t bond with it, then the filament gets used up as fast as in a regular incandescent. The result is simply a very expensive light bulb that lasts about as long as any cheaper bulb. Now, it might be true (and if anyone has some solid information, it’d be good to know) that if you have the light on at full blast for a while and only occasionally turn it low, you can still prolong the life of the bulb. It is clear, though, that leaving it always at dim is not the best thing to do.
Is the dimmer switch buzzing or the bulb?
Cheap dimmer switches can induce a lot of high frequency energy in the AC line. Some dimmer switches employ low pass filters that reduce the high frequency energy.