The first important piece of evidence came from geology. We know now that the earth is old—4.6 billion years, to be exact—but this was not always common knowledge. Prior to the Enlightenment, most people accepted biblical accounts of creation, which placed the origin of the earth around 6,000 years ago.
Now, 6,000 years might sound like a lot, but here was the problem: thinkers in the mid-1700's sat in their favorite armchairs, reading accounts from ancient scholars describing species of animals and plants in Europe 2,000 years earlier. Then they stood up, stretched, and went outside for a walk, and observed those same species virtually unchanged! They came back inside, and over a nice snack, thought to themselves, "If species haven't changed in 2,000 years and the earth is only 6,000 years old, there's no way enough time has passed for evolution to have happened." Enter James Hutton, the father of modern geology.
James Hutton (1726-1797), a Scottish physician by training, had a keen interest in the natural world. In the process of preparing his land for farming, he became interested in geology. Geology is the study of the materials and processes that shape the earth, as well as the earth's history. Hutton realized that wind and water wear down rock, and that over immense periods of time, deposits of those sediments form new layers of rock, which in turn eventually erode again. He also realized the importance of volcanic processes in shaping the earth's features.
Hutton's observations of these geological processes led him to the concept of uniformitarianism—the idea that the same gradual processes that are at work today, like erosion and sedimentation, were at work in the past. Over long periods of time, these processes can produce huge changes in the earth's features—think of the Grand Canyon. Uniformitarianism replaced catastrophism—the idea that sudden, short-term, catastrophic events were responsible for shaping the earth's surface.
The principle of uniformitarianism was popularized by another prominent Scottish geologist, Charles Lyell (1797-1875). Lyell's most famous work, Principles of Geology, built upon the conceptual framework that Hutton had established, providing additional evidence that the earth's features had been shaped by gradual processes still observable today. Lyell was a geology nerd—upon getting married, he took his new wife on a geological expedition for their honeymoon, and no, she did not immediately divorce him once they got home. Smooth move, Lyell. Also on the topic of Lyell's social life, he and Darwin were friends, and Darwin's musings on natural selection were profoundly influenced by the idea of uniformitarianism.
Hutton and Lyell laid important groundwork for evolutionary thought; geology and the principle of uniformitarianism were critical in showing that the earth had, indeed been around long enough for evolution to occur. Once the earth's antiquity was established, it was no longer reasonable to reject evolution on the grounds that the earth was simply too young.
How does Sheldon of the Big Bang Theory feel about geology?