Music was a part of a good education- the Quadrivium was arithmetic, geometry, music and astronomy. As the Church did much of medieval education, you could say that it provided the biggest music school. Modern notation is a creation of Guido of Arrezzo, who created a good way to note rhythm. His method of naming the notes and assigning the note names to parts of the hand ( which evolved into the Guidonian Hand) was a very important part of music education into the 16th c., and it was very common for musicians to work with a part, and they often seemed to work without the printed music in front of them, memorizing a part with the use of hand signals. The Church itself needed musicians, at least singers who could sing pieces like the In Nomines and Agnus Deis of the mass. Famous composers did also have students: Leonin in Paris at Notre-Dame had Perotin , for example, and later Ockeghem had Josquin de Prez.

Secular music had an effect on religious music, but there is much more religious music that has survived than secular, especially instrumental pieces - so it's hard to gauge how much. But they were not averse to using a good tune. For example , there was a very popular song, L'Homme Armé ( The Armed Man) and Johannes Ockeghem, Josquin de Prez and Guillaume Dufay all took the melody for a mass - known still as Missa L'Homme Armé . But it is hard to divide secular and religious at this point in history, anyway: a merchant preparing for a voyage would pay for a mass and bring some holy relics for his trip much like he would also take food and some warm clothes. That merchant would not mind having a mass sung to the tune of the latest catchy song.