Anyone reading this blog has probably been able to read for so long that the memory of first figuring out that those marks on the paper meant words and sounds is, at best, dim. We take reading for granted, but it was certainly not the case before more-or-less universal education and affordable books and libraries.
Being able to read was restricted to the upper levels of medieval society: not just the churchmen and churchwomen, but aristocrats and merchants. Although late antiquity/the Merovingian era had been a literate age, as most transactions were recorded in writing and stored away in municipal archives. Yet when urban civilization collapsed in the early Middle Ages, being able to read became much less useful.
Interestingly, in the late Middle Ages/Renaissance period, anyone who could afford it sent their sons to school and recorded all sorts of events and activities in writing. Notaries flourished, and their records are a treasure-trove for modern historians.
In between the early and late Middle Ages, reading was a much more widespread skill than writing. We tend to think of them as going together, but plenty of medieval people who could puzzle their way through the Latin of a charter would have been hard-pressed actually to produce one. Charlemagne, who read Latin and who could speak Old French and Old German (neither was really a written language yet), could not write. He had taken it up too late and lacked the fine muscle control needed for a stylus or quill pen. His biographer told the charming story of the emperor waking up at night and practicing with a stylus on a wax tablet, in case he suddenly got the knack.
Children in well-to-do households got their first education from their mothers. Boys would generally graduate to a teacher or tutor (often in someone else's house, if for example they entered a monastery or were training for knighthood or were an apprentice in a guild). Girls generally stuck with Mom unless, as sometimes happened, they entered a nunnery as a day pupil.
Being able to read Latin was necessary because Latin was the language of learning and of law, as well of course as the language of Christianity. By the twelfth century one was also taught the vernacular--Old French, Old German, Old Italian, and so on. This was the language of literature, of stories, of epics and romances (on which see more here).
The well-to-do could and did learn to write the vernacular, both to keep track of things and to compose stories and songs to entertain others. The epics and romances were meant to be read out loud (most were written in verse), to wile away long winter evenings.