"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.