Determining the Age of the Earth
As far back as 500 BC, Herodotus of Egypt recognized the build up of silt from the Nile, identifying it as an early geological process. Aristotle (384-322 BC) realized that fossil seashells from rocks were similar to those found on the beach, indicating the fossils were once living animals. He deduced that the positions of land and sea had changed and thought these changes occurred over long periods of time.
Renaissance Geology
Leonardo da Vinci (1452-1519) recognized that material carried by
rivers to the sea was eventually compacted into sedimentary rock and
later uplifted to form mountains. He concurred with Aristotle's view
that fossils were the remains of ancient life. He studied the deposits
of the Po River and concluded that they must be at least 200,000 years
old. 
Catastrophism, Uniformitarianism in the early 18th century
Catastrophism, proposed by Baron Georges Cuvier, suggested that the earth was 6,000 years old (based on 17th century biblical accounting), and that geologically only catastrophic events had changed the geological structure of the earth. (Cuvier's Catastrophism fit well into the biblical schemata of the time, and accounted for the discoveries of many "funny looking bones" found throughout Europe and other parts of the world (commonly known today as dinosaur bones and fossils). Cuvier's catastrophic model explained changes seen within fossilized bones as a result of catastrophic change where less perfect species were wiped to give rise to a new species.Uniformitarianism, promoted by Charles Lyell and James Hutton, stated that changes within the Earth are a direct cause of uniform events, such as erosion and earthquakes. The same processes which have existed within the past occur at the same gradual rate as they do within the present. Contrary to Catastrophism, the events that occurred due to geological change did not correspond directly to biblical events, rather they were a result of uniform events, which had existed since the earth's creation. Hutton and Lyell's theory was the first to assume upon non-biblical terms that the age of the earth was beyond 6,000 years.
The Start of Modern Geology
William Thomson (aka Lord Kelvin) (1824-1907) performed a seemingly flawless calculation which indicated
that the Earth had not existed for eternity but had cooled from a molten state over ~100 million years.
Pierre and Marie Curie (1867-1934) discovered radium (1898) which led to a new tool (measuring radioactive
decay) for absolute dating of certain rocks.
Bertram Boltwood (1907) dated the Earth's age as somewhere between 400 million and 2.2 billion years using
the radioactive decay method.