Here is the Wikipedia synopsis of vermiculture or vermicomposting.
Vermicompost is the product or process of composting utilizing various species of worms, specifically red wigglers, white worms, and earthworms creating the heterogeneous mixture of decomposing vegetable or food waste, bedding materials, and pure vermicast produced during the course of normal vermiculture operations. Vermicast, similarly known as worm castings, worm humus or worm manure, is the end-product of the breakdown of organic matter by the species of earthworm.
Containing water-soluble nutrients, vermicompost is an excellent, nutrient-rich organic fertilizer and soil conditioner. The process of producing vermicompost is called vermicomposting.
What I have discovered in this process are these things. This is not rocket science. Worms are hard workers but a little finicky. And this is not a smelly, dirty, or disgusting thing thus far.
You must use a particular type of worms and I got ours from Uncle Jim’s Worm Farm online. However they do not have a number you can call about problems so I would recommend redwigglers.com. Here is more Wikipedia info about the worms.
The earthworm species (or composting worms) most often used are Red Wigglers (Eisenia foetida or Eisenia andrei), but European nightcrawlers (Eisenia hortensis) also may be used. Users refer to European nightcrawlers by a variety of other names, including dendrobaenas, dendras, and Belgian nightcrawlers.
Blueworms (Perionyx excavatus) may be used in the tropics. However, P. excavatus worms are not suitable for worm compost bins in most of the contiguous United States.
These species commonly are found in organic-rich soils throughout Europe and North America and live in rotting vegetation, compost, and manure piles. They may be an invasive species in some areas. As they are shallow-dwelling and feed on decomposing plant matter in the soil, they adapt easily to living on food or plant waste in the confines of a worm bin.
Composting worms are available to order online, from nursery mail-order suppliers or angling (fishing) shops where they are sold as bait. They can also be collected from compost and manure piles. These species are not the same worms that are found in ordinary soil or on pavement when the soil is flooded by water.
We bought a composting box kit– a homemade one is just as good. What I have discovered are these few things. Worms are not really fond of citrus peels. You cannot include meat or oils. They need their bedding moist but not wet. You can gauge this by the newspaper on top. If it starts to dry out then the bin needs more water. If the worms are moving on top of that newspaper then it is too wet. Here is more info on worm farming.
For vermicomposting at home, a large variety of bins are commercially available, or a variety of adapted containers may be used. They may be made of old plastic containers, wood, Styrofoam, or metal containers. The design of a small bin usually depends on where an individual wishes to store the bin and how they wish to feed the worms.
Some materials are less desirable than others in worm bin construction. Metal containers often conduct heat too readily, are prone to rusting, and may release heavy metals into the vermicompost. Some cedars, Yellow cedar, and Redwood contain resinous oils that may harm worms, although Western Red Cedar has excellent longevity in composting conditions. Hemlock is another inexpensive and fairly rot-resistant wood species that may be used to build worm bins.
Bins need holes or mesh for aeration, and a spout or holes in the bottom for excess liquid to drain into a tray for collection. Worm compost bins made from recycled or semi-recycled plastic are ideal, but require more drainage than wooden ones because they are non-absorbent. However, wooden bins will eventually decay and need to be replaced.
Small-scale vermicomposting is well-suited to turn kitchen waste into high-quality soil amendments, where space is limited. Worms can decompose organic matter without the additional human physical effort (turning the bin) that bin composting requires.
Composting worms which are detritivorous (eaters of trash), such as the red wiggler Eisenia fetidae, are epigeic (surface dwellers) together with symbiotic associated microbes are the ideal vectors for decomposing food waste. Common earthworms such as Lumbricus terrestris are anecic(deep burrowing) species and hence unsuitable for use in a closed system. Other soil species that contribute include insects, other worms and molds.
Climate and temperature
The most common worms used in composting systems, redworms (Eisenia foetida, Eisenia andrei, and Lumbricus rubellus) feed most rapidly at temperatures of 15–25 °C (59-77 °F). They can survive at 10 °C (50 °F). Temperatures above 30 °C (86 °F) may harm them.  This temperature range means that indoor vermicomposting with redworms is suitable in all but tropical climates. (Other worms like Perionyx excavatus are suitable for warmer climates.) If a worm bin is kept outside, it should be placed in a sheltered position away from direct sunlight and insulated against frost in winter.
It is necessary to monitor the temperatures of large-scale bin systems (which can have high heat-retentive properties), as the feedstocks us
ed can compost, heating up the worm bins as they decay and killing the worms.
There are few food wastes that vermicomposting cannot compost, although meat waste and dairy products are likely to putrefy, and in outdoor bins can attract vermin. Green waste should be added in moderation to avoid heating the bin.
Small-scale or home systems
Such systems usually use kitchen and garden waste, using “earthworms and other microorganisms to digest organic wastes, such as kitchen scraps”. This includes:
■ All fruits and vegetables (including citrus and other “high acid” foods)
■ Vegetable and fruit peels and ends
■ Coffee grounds and filters
■ Tea bags (even those with high tannin levels)
■ Grains such as bread, cracker and cereal (including moldy and stale)
■ Eggshells (rinsed off)
■ Leaves and grass clippings (not sprayed with pesticides)
Large-scale or commercial
Such vermicomposting systems need reliable sources of large quantities of food. Systems presently operating use:
■ Dairy cow or pig manure
■ Sewage sludge
■ Agricultural waste
■ Food processing and grocery waste
■ Cafeteria waste
■ Grass clippings and wood chips
Worms in a bin being harvested
Vermicompost is ready for harvest when it contains few-to-no scraps of uneaten food or bedding. There are several methods of harvesting from small-scale systems: “dump and hand sort”, “let the worms do the sorting”, “alternate containers” and “divide and dump.” These differ on the amount of time and labor involved and whether the vermicomposter wants to save as many worms as possible from being trapped in the harvested compost.
While harvesting, it’s also a good idea to try to pick out as many eggs/cocoons as possible and return them to the bin. Eggs are small, lemon-shaped yellowish things that can usually be picked out pretty easily with the naked eye.
Vermicompost has been shown to be richer in many nutrients than compost produced by other composting methods. It also has outperformed a commercial plant medium with nutrients added, but needed adjustment for magnesium and pH.
However, other studies have shown that the effects of home made, backyard, vermicompost compared to municipal compost were lower in terms of soil microbial biomass, soil microbial activity, and yields of a species of ryegrass.
Further, one study concluded that the differences between methods of composting were in large part due to the feedstock, and therefore no generalizations can be made between composts made from varying materials.
It is rich in microbial life which converts nutrients already present in the soil into plant-available forms.
Unlike other compost, worm castings also contain worm mucus which helps prevent nutrients from washing away with the first watering and holds moisture better than plain soil .
■ Improves its physical structure
■ Enriches soil with micro-organisms (adding enzymes such as phosphatase and cellulase)
■ Microbial activity in worm castings is 10 to 20 times higher than in the soil and organic matter that the worm ingests 
■ Attracts deep-burrowing earthworms already present in the soil
■ Improves water holding capacity
■ Enhances germination, plant growth, and crop yield
■ Improves root growth and structure
■ Enriches soil with micro-organisms (adding plant hormones such as auxins and gibberellic acid)
■ Biowastes conversion reduces waste flow to landfills
■ Elimination of biowastes from the waste stream reduces contamination of other recyclables collected in a single bin (a common problem in communities practicing single-stream recycling)
■ Creates low-skill jobs at local level
■ Low capital investment and relatively simple technologies make vermicomposting practical for less-developed agricultural regions
■ Helps to close the “metabolic gap” through recycling waste on-site
■ Large systems often use temperature control and mechanized harvesting, however other equipment is relatively simple and does not wear out quickly
■ Production reduces greenhouse gas emissions such as methane and nitric oxide (produced in landfills or incinerators when not composted or through methane harvest)
Mid-scale worm bin (1 m X 2.5 m up to 1 m deep), freshly refilled with bedding
Vermicompost can be mixed directly into the soil, or seeped in water and made into a worm tea by mixing some vermicompost in water, bubbling in oxygen with a small air pump, and steeping for a number of hours or days.
The microbial activity of the compost is greater if it is aerated during this period. The resulting liquid is used as a fertilizer or sprayed on the plants.
The dark brown waste liquid, or phytotoxin content and organic acids that may be toxic to plants.
The pH, nutrient, and microbial content of these fertilizers varies upon the inputs fed to worms. Pulverized limestone, or calcium carbonate can be added to the system to raise the pH.
Worms and fruit fly eggs under the lid of a home worm bin.
When closed, a well-maintained bin is odorless; when opened, it should have little smell – if any, the smell is earthy. Worms require gaseous oxygen. Oxygen can be provided by airholes in the bin, occasional stirring of bin contents, and removal of some bin contents if they become too deep or too wet. If decomposition becomes anaerobic from excess feedstock added to the bin in wet conditions; or layers of food waste have become too deep, the bin will begin to smell like ammonia.
If decomposition has become anaerobic, to restore healthy conditions and prevent the worms from dying, the smelly, excess waste water must be removed and the bin returned to a normal moisture level. To do this, first reduce addition of food scraps with a high moisture content and second, add fresh, dry bedding such as shredded newspaper to your bin, mixing it in well.
Pests such as rodents and flies are attracted by certain materials and odors, usually from large amounts of kitchen waste, particularly meat. By eliminating the use of meat or dairy product in your worm bin you decrease the possibility of pests.
In warm weather, fruit and vinegar flies breed in the bins if fruit and vegetable waste is not thoroughly covered with bedding. This problem can be avoided by thoroughly covering the waste by at least 2 inches of bedding. Maintaining the correct pH (close to netural) and water content of the bin (just enough water where squeezed bedding drips a couple of drops) can help avoid these pests as well.
Having worms escape is one of the most feared outcomes for many new vermicomposters. Worms generally stay in the bin, but may try to leave the bin when first introduced, or often after a rainstorm when outside humidity is high. Maintaining adequate conditions in the worm bin and putting a light over the bin when first introducing worms should eliminate this problem. 
Commercial vermicomposters test, and may amend their products to produce consistent quality and results. Because the small-scale and home systems use a varied mix of feedstocks, the nitrogen, potassium and phosphorus content of the resulting vermicompost will also be inconsistent. NPK testing may be helpful before the vermicompost or tea is applied to the garden.
In order to avoid over-fertilization issues, such as nitrogen burn, vermicompost can be diluted as a tea 50:50 with water, or as a solid can be mixed in 50:50 with potting soil.
Some sources claim that the mucus creates a natural time release fertilizer which cannot burn plants.]
Here is the composting bins that we bought:
Expandable Worm Tower Worm Compost Bin
I like this composter but if you get one like it, make sure you put 3 or more layers of newspaper on the bottom to make sure the worms don’t constantly burrow out of the bottom screen.
I have not done it yet but when you start the 2nd bin which goes on top of the 1st, I understand the best way to lure the worms to the new bin is very ripe banans. They will move to the new bin because they love bananas.