How did the ideas and beliefs of the Renaissance help lead to the Reformation and the Scientific Revolution?
The Renaissance refers to a period of time beginning in Italy in the mid-1300's where the intellectuals of society looked back to Greek and Roman cultural elements for inspiration on artistic and intellectual pursuits (this was known as humanism). This movement towards education and culture was, on its own, a big change in western European education; prior to this cultural awakening, any education for western Europeans was through the church, and you can expect that the all-powerful Catholic Church in the High Middle Ages was not particularly secular.
The printing press, coupled with a rekindling of education and forward-thinking, allowed for greater literacy throughout Europe. In turn, people began to analyze and critically review literature for themselves, instead of having it read to them. This was the case of the Protestant Reformation. One monk named Martin Luther was particularly outspoken against some of the Catholic Church's reforms. Of his famous "95 theses", which listed all of his grievances with the church, was the idea that people should not have to "pay" their way into heaven by absolving their sins with a document bought from their local preacher. Martin Luther encouraged people to read his 95 theses (printed on a handy pamphlet, thanks to the printing press), and also encouraged them to read the bible for themselves in order to see what needs to be done to be a good Christian. So, we can thank literacy, an increased focus in culture and education, and the printing press for getting the Protestant Reformation started. Martin Luther's (and other reformists such as John Calvin) ideas were printed and widely disseminated throughout Europe.
The increased focus on education also encouraged scientists to take a closer took at the ideas of reason and logic vs. the Church. Some, like Copernicus, reevalutated Greek concepts such as heliocentrism. Others, such as Rene Descartes and Isaac Newton, established a scientific-based approach to knowledge. Scientific approaches, instead of religious approaches, became a popular movement in Western education. This was also made possible by the renewed trade agreements with the East, who at this point in time were miles ahead of Western Europe in terms of technological development and intellectual, reason-based education. So, the Renaissance's insistence on culture, literacy, education, and revisiting elements of Greek and Roman culture (including for this example the astronomical and scientific discoveries) enabled the Scientific Revolution.
Although the Protestant Reformation and the Scientific Revolution were different in many ways, they can both be traced back to the ideas that became more prevalent in Europe during the Renaissance.
During the Renaissance, people came to question authority much more than they ever had before. They came to expect that there should be proof, or logical explanations for various things that happened in the world. In other words, they came to be more inclined towards skepticism and towards independent thinking.
Both the Reformation and the Scientific Revolution can be seen as offshoots of this trend. The Reformation came about because people questioned the authority of the Catholic Church and the logic of its teachings. The Scientific Revolution came about because people wanted proof about things in nature. They no longer wanted to believe, for example, that the Earth was the center of the universe simply because the Bible seemed to say so and because classical authorities such as Aristotle said so.
The Renaissance brought about a trend towards people thinking for themselves. This trend helped to cause the Reformation and the Scientific Revolution.