Ok i'm going to answer the questions in reverse order.sorellavanh said:
Small consumer sized inverters are usually available from camping/outdoor/4x4 shops. Or if you feeling a little brave with electronics then you can make one from an old UPS (cause thats basically all a UPS is)
Depending on the quality (and of course price) of the inverter will affect how good quality the AC electric waves are. Simple electric lights are not at all fussed with a bad quality wave with lots of strange harmonics and steps. Electronic goods however are sometimes not as forgiving. Generally the inverters available these days are sufficient but you may notice added buzzing in sound setups and maybe fuzzy picture quality on the home theatre system. But it is at your own risk and there is always a change that you pop your gear - then again... all the power spikes that come with all the power failures may have done that already
How the inverter works - basically: Transformers can step voltages up and down very easily - but only if the current is alternating. Power out of the plug socket is alternating (AC) hence how you can get cheap, easy power supplies that will give you virtually any voltage you want... and the circuitry to rectify it to a DC (direct current) power source is fairly cheap and simple.
However - batteries only give out DC and putting DC into a transformer will give you nothing out. So what the inverter does is take power from the battery and using some clever electronics produces a low voltage AC wave that can then be stepped up through a transformer and come out at the standard 220(ish) volts.
