The most important timekeeper of the medieval world were churches--the parish church and cathedrals, of course, but especially churches affiliated with a monastic/mendicant order or with a chapter of canons (semi-monks) attached. Their bells would sound to announce the Hours--the designated periods of prayer throughout the day prescribed by monastic Rules.

When mechanical clocks and hourglasses appear and spread throughout western Europe in the 14th and 15th centuries, indeed, monasteries are a major channel of dissemination. But monasteries still had need of counting the hours--the Hours--before then.

The two basic methods were not unique to western Europe. First was the water clock. What used to be thought (i.e. what Wikipedia still thinks, citing books from the 1800s) references to mechanical clocks in the Latin West prior to the 13th century are typically now understood to be water clocks, sort of like an hourglass with water instead of sand. (Medieval Arab scientists would adapt water clocks into a mechanized form. It took the West longer than the Islamic world or the Greek East to figure out how to use mechanical gears to move things without ongoing human intervention.)

The second was the candle or lamp clock, which used the burning-down of a candle (with the size calibrated and standardized) or the depletion of lamp oil to measure periods of time.

But it can't be that simple, can it?

Water clocks and candle clocks kept equal increments of time, and the medieval monastic Hours were not equally spaced. They shifted to accomodate sunrise, sunset, and the rhythms of monastic life (or, as Le Goff has posited, the demands of daily labor in general, particularly in cities). Indeed, the length of an 'hour' differed throughout the day and throughout the year. (Not to mention over the course of the Middle Ages.)

ETA: McCluskey, "Gregory of Tours, Monastic Timekeeping, and Early Christian Attitudes to Astronomy" talks about some of the problems medieval monks dealt with between hours of set, regular duration, and variable hours based on the length of the day and the night shifting throughout the year.