Similia Similibus Curentur
"like heals like" was a principal, espoused by Aristotle, Hippocrates and others throughout the ages. It means we should be looking for the remedy that would, in a healthy individual, produce "similar suffering" to what our patient is experiencing.
Homeopathy is a science-based system of medicine based on the discoveries and observations of 19th century German physician and chemist, Samuel Hahnemann. This safe and effective treatment method uses the principle of 'similars,' or 'like cures like,' from which its name is derived. As such, Hahnemann cured illness using the smallest possible doses of a medicinal substance that creates similar symptoms in a healthy individual.
Single Simple Remedy
From that day to this, classical homeopaths have used the Law of Similars, and the principal of the minimum possible dose, to diagnose and treat their patients: either human or animal. During a consultation a patient's entire medical history is explored, and the totality of symptoms considered. Only after this, is a single, simple remedy chosen. This remedy, if well-selected, will gently stimulate the body's own healing mechanisms to bring about recovery.
Homeopathic medicines are made by a unique method of serial dilution and succussion (vibration). The result is micro-dose, 'potentized' remedies that make extremely safe, effectual medicines.
Scientific Evidence for Homeopathy
Homeopathy's effectiveness in a wide range of conditions is increasingly being verified by high quality clinical and laboratory trials, both human and animal. Recently the Swiss Government decided the body of evidence was great enough to justify incorporating homeopathy into the national health care system. See here for full story.
Another interesting article.