I was telling mstevens about the worms I have living on my balcony, and he said I should tell ewtikins about them too. So I decided to tell all of you. This is basically a copy and paste from my email; sorry m, you get to see it twice :)
We've got a wormery composter on the balcony. It's basically two stacking boxes, and a pile of worms (red worms, Eisenia fetida). You start it off by lining one box with a thin layer of shredded newspaper and adding the worms. Then you give them 2–3 days to settle down before you start feeding them. You feed them by spreading a layer of vegetable waste on top, and covering it with more shredded newspaper. The newspaper adds carbon (the carbon-nitrogen balance is rather important, apparently), and keeps fruit flies away (not entirely successfully in our case). When the box is full, you take out half the worms and use them to start the other box; the full box gets left alone for a few months for the worms to finish the composting process.
Yesterday, we did the “taking out half the worms” part. They're very good at avoiding fingers. There were little baby worms in there too! So cute!
We generate quite a lot of veg peelings, so I may get more boxes and worms, if I manage not to kill this lot. They stack on top of each other so it won't use up more space.
This page about vermicomposting has more info. If you're interested, see if your local council has a discount scheme to encourage residents to compost; we got our wormery for only £8 including delivery (and worms!) via Southwark council.
Update: some useful hints on dealing with fruit flies (thanks Miki!)