Darwin spent five years on his journey as the ship's naturalist on the H.M.S. Beagle. Some of the evidence he used to support his theory was based on fossils he saw in South America. In the 1800's, most people were of the belief that the world was only a few thousand years old and that organisms that existed were unchanged since the beginning. However, the fossil evidence that he found showed giant versions of modern animals that no longer existed. It pointed to the idea of an ancestor that may have changed over time to the modern life forms that exist today. He also noted that the most likely place that the life forms on the Galapagos Islands could have come from originally, was Equador which was about 600 miles away. Differences in environment, food supply, temperature, etc. would put different pressures on animals on each of the various islands. Over time, natural selection would favor those best adapted for their various environments and after two million years, you have many different species that have evolved from common ancestors in Equador. The most famous of course, are Darwin's finches. Also famous are the different giant tortoises that vary by shells, size and habits, from island to island. Other famous animals include iguanas. One is extremely unique, the marine iguana, which is the only marine iguana in the entire world.
The most famous example of evidence that Charles Darwin used to support his theory of natural selection is the example of the finches in the Galapagos Islands. These finches had evolved in ways that showed natural selection at work.
Basically, the finches were all descended from a common ancestor that had gotten stranded on the Galapagos, isolated from South America. Once there, they evolved to fill many ecological niches that were empty. This evolution could be found in the shapes of their beaks.
Each species of finch had evolved a new shape and size of beak. This beak shape and size was dependent on what sort of food this species had specialized in eating. This showed that the finches with the most adapted beaks for each kind of food succeeded and gradually ended up becoming new species.