How did Europeans’ conceptions of knowledge change during the Scientific Revolution and the Enlightenment?

The conception of how to acquire knowledge really changed during the Renaissance with the advent of Humanism. Though this cultural revolution is less clearly understood today, one of the main ideas within Humanism is that most of humankind's problems can be solved through rational thinking. This view was sustained in the succeeding centuries, allowing for the development of the Scientific Revolution in the sixteenth- and seventeenth-centuries and the Enlightenment in the eighteenth-century.
Humanist belief also allowed for thinkers to question the supposed infallibility of the Church and religious doctrine. The Catholic Church insisted on the geocentric vision of the universe -- that is, that Earth was at the center of the universe. This view was challenged by Nicolaus Copernicus in 1543 in his book, On the revolutions of the heavenly bodies. Galileo Galilei developed Copernicus's heliocentric theory, or the fact of the sun being at the center of the universe, but would remove those key passages from his book, De revolutionibus, at the insistence of the Church, which had accused him of heresy. The prohibition was not dropped until 1835.
However, the damage had been done. Scientists were challenging Scripture, as well as the accepted, but erroneous, ideas of the ancient thinkers. This curiosity only fomented more curiosity. Soon, studies of anatomy developed under scientist Andreas Vesalius. The body was no longer a site of sin, but one of wonders. Johannes Kepler continued studies of the universe, discovering that the Earth's movements around the sun were not circular, but elliptical. 
The willingness to challenge the continent's most important institution also extended into politics and ethics. What were a human being's natural rights? Were human beings innately good or bad? If innately good, were we corrupted by society, which caused all of our ills? These questions were explored by the political thinkers John Locke, Thomas Hobbes, and Jean-Jacques Rousseau. 
After contemplating human nature, they began to wonder about the best possible form of government for a nation: absolute monarchy, as Hobbes had insisted, or a more democratic society based on notions of personal liberty, as Locke would have it. History has sided with Locke. Thinkers who more specifically developed ideas about government include Thomas Paine, Alexis de Tocqueville, and the legal scholar, Montesquieu.
Overall, the Scientific Revolution and the Enlightenment permanently de-legitimized the presumed infallibility of the Church. Renaissance humanists were outliers; most people dared not question Church authority. These cultural movements also encouraged an unprecedented engagement with the natural world and with society.