I've been vermicomposting for years now. The compost you get at the end is absolutely fantastic, but the volumes are not enormous, so you'll probably find yourself distributing it parsimoniously.
I have a can o' worms or however it's spelt. The worms make a minor bid for escape whenever it rains but are never very successful unless I leave the tap open! What I do find, however, is worms all around the inside of the lid in wet weather. But if you're keeping it out in the garden, it won't matter if a few do somehow manage to get out. I certainly don't feel the need to cover it up in the way that stevens706 does.
When the weather is very hot, if your wormery is in an exposed spot, it can help to give it a bit of shade with a piece of horticultural fleece on top (not tied down) or even to pour some cool water inside it (fantastic worm tea emerges at the bottom - tea for the plants not you, obviously!). The worms are surprisingly able to cope with cold weather.
My big dilemma is when it comes to sorting the compost from the worms: despite the can o' worms selling point being that the worms make their way upwards towards the latest stuff you've put in, there are still worms in among the compost you want to remove. The dilemma is: how long are you prepared to spend sorting worms from compost vs. how many worms are you prepared to sacrifice?
Worms will deal with most vegetable waste from the kitchen, though they're not too fond of the onion or citrus families. At one stage, I tried giving them fish skin and bones, but the largest of the bones remained lethal to the fingers for some time! Plus it was a bit smelly, though not as bad as you'd expect. I've never given mine meat waste. I don't give them fruit waste at certain times of year because I don't want to attract wasps.
You'll soon get to know the things that worms love - any soft squidgy stuff, tea bags, coffee in filter papers, etc. Egg shells are popular with worms, though you'll want to crush them a bit before you put them in as they are very slow to break down.
You'll see lots of other organisms in your wormery. Most of them are beneficial and in fact help to break down the kitchen waste to a state where the worms can ingest it.
I'm sure lots of other people will have stuff to add to this, but feel free to ask any questions. A book I found useful is "Worms Eat My Garbage", by Mary Appelhof.