I use a bin in the kitchen that's similar to (though smaller than) the one that TealGreen described. We bought it at an "organizer store" (I forget the name of the place.) I like the smaller size because it encourages me to take compost out more frequently!
As to the actual composter, I built dry-laid brick and block walls in the back yard to contain compost heaps. (The brick and block were 'leftovers,' so the compost heaps were more or less free.) There are two, probably about four feet by four feet.
Our volume of compost ingredients isn't enough to generate the high temperatures that true composters strive for, so it's really more of a worm bed, I suppose. That's one reason that we have two heaps: one's active, and the other one is 'aged' and can be drawn upon for planting soil.
As TealGreen says, avoid meat scraps and the like. We also avoid citrus peels, as we're advised that they don't break down well. Corn cobs do, eventually, but take quite a while. Eggshells are OK, though, once again, slower to break down than most.
We're pretty satisfied with our little system. Little fuss or muss, and it turns out beautiful black, rich soil (and lots of earthworms!)