Diluting substances as much as homeopathy does would not only vastly decrease any effects the substance in question has, but in fact completely destroy the healing agent. Robert L. Park, Professor of Physics and director of the Washington office of the American Physical Society, writes in his book "Voodoo Science: The Road from Foolishness to Fraud":
[Samuel] Hahnemann [the 18/19th century "inventor" of homeopathy] used a process of sequential dilution and to prepare his medications. He would dilute an extract of some "natural" herb or mineral, one part medicine to ten parts water, or 1:10, shake the solution, and then dilute it another factor of ten, resulting in a total dilution of 1:100. Repeating that a third time gives 1:1000, etc. Each sequential dilution would add another zero. He would repeat the procedure many times. Extreme dilutions are easily achieved by this method.
The dilution limit is reached when a single molecule of the medicine remains. Beyond that point, there is nothing left to dilute. In over-the-counter homeopathic remedies, for example, a dilution of 30X is fairly standard. The notation 30X means the substance was diluted one part in ten and shaken, and then this was repeated sequentially thirty times. The final dilution would be one part medicine to 1,000,000,000,000,000,000,000,000,000,000 parts of water. That would be far beyond the dilution limit. To be precise, at a dilution of 30X you would have to drink 7,874 gallons [30 m³] of the solution to expect to get just one molecule of the medicine.
Compared to many homeopathic preparations, even 30X is concentrated. Oscillococcinum, the standard homeopathic remedy for flu, is derived from duck liver, but its widespread use in homeopathy poses little threat to the duck population -- the standard dilution is an astounding 200C. The C means the extract is diluted one part per hundred and shaken, repeated sequentially two hundred times. That would result in a dilution of one molecule of the extract to every 10400 molecules of water -- that is, 1 followed by 400 zeroes. But there are only about 1080 (1 followed by 80 zeroes) atoms in the entire universe. A dilution of 200C would go far, far beyond the dilution limit of the entire visible universe! 
Park points out that Hahnemann was likely unaware of exceeding the dilution limit because he did not know about Avogadro's number, a physical constant which makes it possible to calculate the number of molecules in a given mass of a substance. Park explains the early success of homeopathy by comparing it with the use of actually harmful remedies at the same time: "Physicians still treated patients with bleeding, purging, and frequent doses of mercury and other toxic substances. If Hahnehmann's infinitely diluted nostrums did no good, at least they did no harm, allowing the patient's natural defenses to correct the problem."
Park further explains how modern homeopathologists agree that there is no actual molecule of medication in their medicine, but that the liquid "remembers" the substance after the process of dilution. How this substance memory is attained has never been explained. Critics also point out that water spontaneously dissociates into acid and alkali (which is why it has a pH of 7). The quantity of acid in a homeopathic remedy, although tiny, is generally higher than the quantity of active agent.