Galileo was the towering scientist of his age, much as Einstein was in the twentieth century. If, as we should, we associate the Renaissance with the beginning of the movement from the centrality of faith to the centrality of reason, he is the exemplar of reason for his period.
Galileo relied completely on what today is understood as the scientific method—direct observation and experimentation—rather than the Bible or received tradition in his study of astronomy. Because he developed the telescope, he was able to study the movement of the planets, discovering the four largest moons of Jupiter and determining that Aristotelean cosmology (a received tradition) was in error, causing a huge stir in the scientific community.
Galileo also studied velocity, dropping balls of different weights (again using the scientific method of direct observation) from the top of the leaning tower of Pisa to time how quickly they fell. He demolished Aristotle's contention that objects of different weights fall at different speeds through experimentation. Stunningly, however, he had no concept of gravity, as Newton, who would discover gravity, had not yet been born.
Galileo's most famous example of himself as exemplar of rationalism and the scientific method came in his bold assertion, based on his years of observation of the planets, that the earth revolved around the sun and not vice versa. This was a radical concept for two reasons: first, the Bible stated that the sun revolved around the earth. The people in the Renaissance were as intelligent as we are and understood that much in the Bible was metaphor, so when scientific evidence refuted Biblical claims, the people of Galileo's time were quite ready to move what they though were literal statements into the category of the metaphoric. (The undeniable realization that the earth was round, for example, moved Biblical references to the four corners of the earth to the realm of metaphor.)
However, there was another problem with Galileo's assertion, in that people had what they thought was the scientific method on their side: the experience of their senses. It seemed completely evident using one's eyes that the the sun proceeding in an orderly orbit around the earth.
Against a deepening backdrop of political trouble in Italy as the pope and the Austro-Hungarian empire suffered losses in the Forty Years war against the German states, a "holy" war that was supposed to assert the supremacy of the universal Roman Catholic church, the pope came under intense pressure to weed out heresy. When Galileo rashly published his theories of heliocentrism (that the planets, including the earth, circled the sun) he became an easy, high profile target to demonstrate that the Church was vigilant about heresy, and he was, under pressure from the Inquisition, forced to retract what he knew from observation, but could not yet (again, remember there was no concept of gravity) prove to be true. Nevertheless, his groundbreaking reliance of the scientific method and courage in asserting his truth have earned him a lasting reputation as the father of modern science.