Mainstream science holds that, generally speaking, the potency of a drug increases with the dose. Which would lead one to conclude that it works best if you don't use any at all. Homeopaths don't say that, of course, but it's the practical impact of the fantastic dilutions they employ. At 30X, chances are that a given dose of the medicine doesn't contain a single molecule of the original, but some dilutions go a lot higher than that. I've heard of one cold remedy with a dilution of 200C, which mathematically is less than one molecule per all the known matter in the universe.
Apologists fall back on far-fetched explanations involving energy and vibrations and so on.
This miraculously unlocks the healing power of the medicinal substance. Could be just my Catholic background talking, but that sounds like making holy water to me. Homeopathy has enjoyed a quasi-protected status ever since, with federal regulators generally taking the view that the practice is harmless and that any attempt to suppress it would likely have political repercussions. There have even been studies in journals with varying degrees of credibility purporting to show that homeopathy actually works. It's silly to believe in homeopathic cures, but I'm not seeing that it's smarter to place your faith in Sudafed instead.