I live in a teeny urban apartment (250 sq ft!) and have a worm bin under my kitchen sink.  It's wonderful.  I use two nested rubbermaid tubs (they probably have vinyl - good luck avoiding that).  There are several cut-out holes in the top lid that I duct-taped window screen material onto, to let air circulate and keep flies out.  I think it would be fun to use clear bins, but mine are dark blue.  I'd also invest in a good sturdy trowel/small gardening shovel with a pointy end so that you can bury the veggie scraps instead of putting them on top.

Everyone I know who's worm-composted has had that dreaded week when they put too much food in and it killed all or most of the worms and created a smelly  mess.  You can avoid this (and I've avoided it for three years now) if you just go slow, put in a little, and see how quickly it disappears, then put in a little more, etc., until you find the limit of your bin.  The worms can go a LONG time without food, so even if you go on vacation, don't load them up beforehand thinking they will starve.

Worms eat more when it's warm, and less when they're cold, so think about that when you plan where they will go.

Umbra et. al. - I'm thinking of having a bin construction party - I'll get all the materials and we'll all put them together at once.  But I don't want to get a bunch of bins w/ vinyl. Any advice on how to determine if there's vinyl in a bin?  Any recommendations of brands/sources without vinyl or other nasty chemicals like BPA?  Thanks - MoxiePixie

You may be able to find a number on the plastic bin.  A bin made of PVC should have a #3 on it.  There's lots of plastic guides on the internet that will tell you which plastics will off-gas & leach less than others.

You may not be able to find a sturdy alternative though.

I've been vermicomposting for ~8 years and have started a bunch of my co-workers vermicomposting too.

I started with the Off-the-shelf design Umbra referred to but made the following modifications
 - bin was smaller W:15" x L:18" x H:15".  Bought two of those rubberneck ones... cheap.
 - made about 12 1" holes in the bottom.
 - covered bottom with screen netting and hot glued with a few glue spots
 - forget about the top vents, impossible to find. Just drill 8 2" holes on the sides close to the top and hot-glue (all round) some moskito netting to prevent flies from getting in.
 - put the prepared bin into the other one.  Use something as a spacer to raise your bin inside ther other one so that the worms don't soak.
 - Forget about the spigot.  Hard to find and you can just take the bin out of the drainage bin and pour the liquid out.

This system can be stacked .  I've got two of these bins at home, stacked.  No one in the house knew about my first one for months.  I even had it at work for a few months without anyone noticing.

Don't worry too much about bedding and all that.  Once they get started... gradually... they'll take whatever you give them even if it's not balanced carbon vs. nitrogen.  Stay away from meats and the other obvious things you'll read about in books and web pages.  Also, I found that onions never decompose that that broccoli stinks it up so I leave that out.

You may have problems with flies occasionally.  If it becomes a problem, vacuum them up and then start wrapping your food scraps in non-colored newspaper (color is toxc) before you put into the bin.  After a week or two, that should solve it.

Another thing I learned the hard way, is to keep their diet a little balanced.  Like once I put a pile of coffee grinds... stank up the place from the mold.  Another time I put a whole rotten cantilope... the vermicompost tea was putrid!  They benefit from variety, just like us :)

Books: I highly recommend either "Worms eat my garbage" (layman) or "the worm book" (a bit more detailed info about worms, cool).

If you ask around, you might find someone that has some worms to get you started.  Don't need much, they'll build up.

Currently have a demo bin at my desk made of 2 peanut butter pastic tubs, 1 month and no smells. ;)

I've been worm-composting for about 2 years now. I started 'cause I wanted to be able to continue composting in the winter time (which you can't really in the northeast). So I started one worm bin in my basement and now I have two...they work much faster than traditional compost bins and I feel strangely protective of them... Do be careful as a beginner to know what you can and cannot feed your worms: no meat, fish or dairy (by)products! Also, get yourself a small bag of GARDENERS lime (not straight lime!) for those weeks when it gets too acidic (one too many grapefruit rinds!) and smells bad. A handful or two every few months keeps the pH more neutral and the wormies happy. Oh, and when you get little flies, it's not your fault...believe it or not their eggs are on the rinds of fruits and veggies when we buy them, and then they hatch in the bin. Yeah, gross...a very good arguement for always washing your produce!

I'm a 20+ year worm composter, and here is the best tip I can give anyone interested in this: use a blender to make your scraps into smoothies before feeding to the worms. If you do this, you will eliminate any problems with smell, flies, mold, and you will get compost much, much faster. Think about how small the worms' mouths are-it is much easier for them to eat up scrap smoothies than big chunks of food. If the scraps are in big pieces, they are definitely going to rot, mold, smell, etc. before the worms can devour them, especially in winter and colder climates. Also, you will not need to worry so much about balancing out the food sources.
It sounds like a lot of work, but it's really not, especially when you get into the habit. I use an old blender with a glass pitcher. During the week, I put scraps straight into the blender I keep on my counter (you can keep it under the sink, if you want). When it is full enough, it takes about 20-30 seconds to blend it with some liquid, and then I pour it into the worm bin. It hardly takes any more time, and the results are fantastic. I believe I have the happiest worms in the world!