The short answer to this question is this: it's nonsense. It isn't considered part of medical science by doctors, and there's a very good reason for this. Firstly, the its claimed "method of action" is illogical and violates the known laws of physics and chemistry. Secondly, and far more damningly, it has persistently been shown, by successive well-constructed trials, not to work. Anyway, if you're looking for a good overview of the topic, a wonderful place to start is this page (from Quackwatch), entitled "Homeopathy: The Ultimate Fake". You really need to read the whole thing, but here's an extract to whet your appetite:
Homeopathic products are made from minerals, botanical substances, and several other sources. If the original substance is soluble, one part is diluted with either nine or ninety-nine parts of distilled water and/or alcohol and shaken vigorously (succussed); if insoluble, it is finely ground and pulverized in similar proportions with powdered lactose (milk sugar). One part of the diluted medicine is then further diluted, and the process is repeated until the desired concentration is reached. Dilutions of 1 to 10 are designated by the Roman numeral X (1X = 1/10, 3X = 1/1,000, 6X = 1/1,000,000). Similarly, dilutions of 1 to 100 are designated by the Roman numeral C (1C = 1/100, 3C = 1/1,000,000, and so on). Most remedies today range from 6X to 30X, but products of 30C or more are marketed.
A 30X dilution means that the original substance has been diluted 1,000,000,000,000,000,000,000,000,000,000 times. Assuming that a cubic centimeter of water contains 15 drops, this number is greater than the number of drops of water that would fill a container more than 50 times the size of the Earth. Imagine placing a drop of red dye into such a container so that it disperses evenly. Homeopathy's "law of infinitesimals" is the equivalent of saying that any drop of water subsequently removed from that container will possess an essence of redness. Robert L. Park, Ph.D., a prominent physicist who is executive director of The American Physical Society, has noted that since the least amount of a substance in a solution is one molecule, a 30C solution would have to have at least one molecule of the original substance dissolved in a minimum of 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 molecules of water. This would require a container more than 30,000,000,000 times the size of the Earth.
Oscillococcinum, a 200C product "for the relief of colds and flu-like symptoms," involves "dilutions" that are even more far-fetched. Its "active ingredient" is prepared by incubating small amounts of a freshly killed duck's liver and heart for 40 days. The resultant solution is then filtered, freeze-dried, rehydrated, repeatedly diluted, and impregnated into sugar granules. If a single molecule of the duck's heart or liver were to survive the dilution, its concentration would be 1 in 100200. This huge number, which has 400 zeroes, is vastly greater than the estimated number of molecules in the universe (about one googol, which is a 1 followed by 100 zeroes). In its February 17, 1997, issue, U.S. News & World Report noted that only one duck per year is needed to manufacture the product, which had total sales of $20 million in 1996. The magazine dubbed that unlucky bird "the $20-million duck."