The word "homeopathy" comes from the two Greek words "omoios" and "pathos", which mean "same" and "disease" respectively. It originated in the 19th century in Germany with physician Samuel Hahnemann, beginning about 1810. For an excellent description, follow this link. You might want to print a copy to study.
In the 19th century, quinine was the marvelous cure for malaria. Hahnemann tried quinine on himself and found that it produced symptoms very much like those of malaria. From this one observation he concluded that "like cures like." To treat a disease you must administer a substance which produces the same symptoms as the disease itself.
This refers to the belief that, as a solution is diluted is becomes more powerful. Dilution by a factor of 10 is indicated by "X" and dilution by 100 is noted by "C". A dilution of "3C" is diluted 100-to-1 3 times for a total dilution of 106 (one million), which is stronger that 1C. Chemists will roll their eyes at this idea, for they know perfectly well how dilution WEAKENS a solution.
This dilution paradigm runs into something very real - Avogadro's Number. This physical constant has a value of 6.023 x 1023. For those who haven't done any chemistry, here's a brief description. All atoms have nuclei made up of protons and neutrons (except hydrogen, which has only 1 proton). The atomic weight is simply the count of protons and neutrons. For example, carbon 12 has 6 protons and 6 neutrons and is the usual isotope of carbon. If we arbitrarily take 12 grams of C12, it will contains 6.023 x 1023 atoms and this quantity will be called one mole of carbon. One mole of iron 56 will weight 56 grams. And so on... One mole of anything will contain Avogadro's Number of atoms (or molecules if apropriate) and will weigh a number of grams equal to the atomic weight of its molecules or atoms
This bit of very real physics produces a dilution limit. If you dilute one mole of anything by 1024, you are not guaranteed to have even one molecule (atom) of the original substance left! In homeopathic terms, 1024 is 12C. On top of this, the pill is produced by putting ONE DROP of the diluted substance onto a lactose tablet.
One Jacques Benveniste thought he had found an explanation for homeopathy. In 1988, he published work claiming that water "remembered" what ever had been dissolved in it before dilution. This got him an "Ignobel" prize TWICE. Read about Benveniste and his work here.
Homeopathic remedies are studied by means of "provings", in which healthy people are given doses of a natural substance and then are observed to see what happens. It must be done this way because the "cure" is supposed to cause the same symptoms as the ailment, making testing on patients impossible.
In the last 15 years or so, homeopathic remedies have been subjected to at least a little regulation by the FDA. They are considered to have little or no active ingredient, and so the regulation is not like that of real drugs. A Google search for "homeopathic fda regulation" will turn up some good references. The homeopathic organization site has good information, as does a government site. They make recommended reading.
Prof. Scalise decided to make sure he did not suffer from insomnia. He had obtained a bottle of homeopathic insomnia remedy (for $11!) at a local store. The safety seal was still intact. Prof. Scalise then proceeded to dump about 2/3 to 3/4 of the pills and swallow them. Took some amount of water to do it, and he reported a chalky taste.
One of the ingredients started at 0.00012% alkaloids. This was diluted 3X, which means 103, or 1,000 times. Final concentration would be 0.00000012%, which is about one part in 109. That's one part per billion. That concentration of almost anything can be detected only by the most sensitive modern tests, if it can be detected at all!
By the way, Prof. Scalise was still wide awake and going at 5:00 that afternoon. The pills had no effect.
This is an old, traditional Chinese technique. It supposedly unblocks the flow of chi by using needles inserted at specific points in the skin. The Skeptic's Dictionary has an excellent overview; be sure to read it.
Chiropractic originated in 1895 with an accidental discovery be a grocer in Iowa. D.D. Palmer manipulated a lump in the spine of a worker and the man's hearing problem cleared up. From this one sample, Palmer concluded that the spine was the center of everything. Misalignments of the spine could, he figured, cause all kinds of diseases. Read this good description for the details.