O.K. We are looking at Worm Farming from two different aspects here:
First, the Worm Farm used principally as a source of vermicast, worm oil and livestock, and second, the Worm Farm used for the disposal of kitchen waste.
That's not to say that the two are mutually exclusive, however the purpose for which you intend using them does have some bearing on how you will have to set things up.
For the first, those kits that can be bought from Nurseries and some DIY stores are actually very good. In fact, I have ten of them - two of the round 'can-o-worms, and eight of the rectangular types.
Maybe a piece I wrote a couple of years ago might be helpful in explaining something of what we set up:
The Composting Compound and Worm Farm.
We have set up an area at the end of the vegetable gardens as a 'composting compound' and worm farm. For general composting I use the traditional method of having three side-by-side bins, which I constructed from treated timber. These are set up in the shade of trees, directly on bare ground. This is important as during decomposition of fresh material the temperature generated can be fatal to worms, however by having no base to the bins, worms are able to go deep out of harms way. They soon come back up when the pile has cooled down. A correct balance of moisture is important too: Too dry, and the thing won't work; too wet and the pile will become a stinking mess that won't work.
Our worm farm consists of ten 'Reln' Worm Farm boxes, and these easily handle most of our kitchen waste, along with a large amount of horse and cow manure, and grass cuttings. It's also important to add a bit of soil to the mix as, having no teeth, worms use it to help them grind the food down. I also occasionally add a shovel full or two of material from the compost bins, not so much to vary the worms diet, but to help add a few trace elements to the vermicast and worm oil. To make the grass cuttings more attractive to the worms, they are first left to dry out, then placed in barrels with a good handful or three of garden lime, and semi-dry horse manure that has been put through the garden mulcher - about two barrow loads of finely mulched grass to one load of manure. Water is added, so that the mix is wet but not soaked, and the barrels capped and left to compost for a couple of weeks, being given a few turns each day. At the end of this process you have barrels about 1/2 full of good compost, or worm food. My theory on this is that the bacterium in the manure, which is enjoyed by the worms, has been carried right through the grass cuttings. You could buy compost tumblers for doing this, but it's cheaper to use the 200 litre plastic barrels that pickles and olives, etc. are transported in, and support them on casters that have perhaps fallen off a shopping trolley. (Although, if your shopping trolley wheels are anything like those used around here, it's anyone's guess where your barrel could go.)
If you want to try worm farming on a small scale to start with, polystyrene boxes that are used to transport broccoli to supermarkets are also good to use as worm growing boxes, and the supermarkets are usually quite happy to part with them. (We call them 'pollycolly' boxes.) At present I am scouring the countryside for three or four more bath tubs to replace my current set-up. By installing these at a comfortable working height, I could also connect their outlets to a common collection pipe to deliver the liquid run-off to storage drums. My old worm farm boxes will then be available for teaching organic gardening at local primary schools. The worms from this project can be used to help feed the chickens, and the fish, whilst the contents of the worm boxes, vermicast, can be safely dug into the organic vegetable garden beds. The liquid drained from the base boxes, (worm oil), is an extremely rich fertilizer, and must be diluted (9:1) with water for use on the gardens, orchards or pastures. (You could also fill plastic containers with it, and sell it to others.) Whacko! – Another source of income!
BTW, The worms used are mainly tiger worms (Eisenia fetida), red worms (Lumbricus rubellus), and occasionally Indian blue worms (Perionyx excavatus). Earthworms, of which there are some 100 species native to the USA, will not, as Atash said, survive in compost farms or compost bins, and neither will compost worms survive very long in garden soil.