Modern science is obsessed with method. The methods used to derive new knowledge then validate that knowledge are key to all scientific work. Most religion and science discussions seem to favour human dramas such as the Galileo Soundbite over discussions of method. Both are important and any discussion ignoring one or the other is suspect.
A key element of Science is the use of induction. Induction deals with attaining new knowledge by generalizing from particular events or objects. Induction has been refined in science to include observing nature, generating a hypothesis from your observations, then testing your hypothesis by experiment.
Galileo and other scientists of his time were champions of the scientific method. While the seventeenth century brought the clearest exponents of the scientific method, there was at least a 350-year tradition in Europe of discussions on the use of inductive techniques very similar to science before the seventeenth century. Roger Bacon, a Franciscan monk, is known to have discussed a sequence of observation, generation of hypothesis ( predictions ), and then demonstration of the hypothesis via experiment. Grosseteste, the Roman Catholic Bishop of Lincoln, was an advocate of inductive techniques as well, considering it the discovery of causes from the study of effects. The techniques used by these 13th century philosophers (and clerics) was to be known as "resolution and composition" and was to be discussed and taught continuously in various parts of Europe between the 13th century and Galileo's time.
Leading innovators in the scientific method such as Zabarella were centred in Padua in the late 16th century; before Galileo arrived there. According to A.C. Crombie, Galileo was influenced in his thinking by the philosopher Zabarella, arriving in Padua only three years after Zabarella's death. A simple explanation of Zabarella's techniques follows "He finds four stages in the process of this regress: observation of the effect; resolving the complex fact into its components and conditions; mental examination of the hypothetical cause to find its essential elements; and demonstration of the effect from that cause." . This is a very similar to the modern view of the scientific method. Zabarella presented it as a philosophical technique but believed the method should be applied to the investigation of nature. The scientific method was not a technique that sprang up magically in the 17th century, as is commonly taught.