"How did monasticism develop in early medieval Europe?"
The two most important steps in the development of Western European monasticism were the creation of the Rule of St. Benedict and the later reform of the Benedictine Order by the Cluniacs.
The Rule of St. Benedict was written sometime in the early 500s AD. It set up a common rule for how Christian monasteries would be set up and how they would conduct their daily affairs. This rule brought order to the Christian monastic movement. It made monasticism repsectable and it gave rise to a number of daughter monasteries that spread across Europe.
Some 400 years later, the Benedictine Rule had lost some of its purity -- Benedictine houses no longer acted with as much piety as they originally did. At this point, the Cluniacs stepped in and started a major reform movement meant to bring monasticism back to its original holy state. This movement helped to restore monasticism's past status in the Church.
Therefore, these were the two most important steps in the development of monasticism in Europe.
I am going to refer you to chapter III of Religion and the Rise of Western Civilization by Christopher Dawson (1950): "The Monks of the West and the Formation of the Western Tradition."
Your school librarian or local public library might be able to borrow this book for you from a nearby university library, or perhaps you can visit a nearby university library. Check in that library's online library catalogue before you make the trip to see if it has this book. The Library of Congress Call Number is BR115 C5D37.