This is actually a common misconception about military confrontations in the medieval period. The medieval period is largely characterized by the "Politics of Land," whereby owners of property could be expected to take up arms to (at least in theory) defend that property. This meant that arms, armor, and the business of warfare, was largely the purview of people who could afford their own arms and armor and had the time to learn how to use them.

Professional soldiers also did not entirely disappear either. They were no longer the centrally managed professional legions of the Roman Empire, but were rather managed locally by important property owners, political appointees, or other grandees in that uncomfortable and vague hierarchy we call "Feudalism." They have various names across european societies: Huscarls, Husjarls, Sargeants, Retainers, as well as others. They could be members of an aristocratic household, or maintain themselves through concessions of land. Their tasks in and around the household could vary, and they could be more or less numerous in different societies or in different kinds of households, but there would always be the expectation that they be well-practiced in use of arms, and travel with their overlord to war if needed.

There were some exceptions that somewhat resemble what you're asking about. In urban communities, citizens otherwise disinterested in fighting might indeed be called up to war. Some of these citizens might be wealthy aristocrats who owned estates outside the city and practiced with arms and armor that they themselves maintained (and wealthy merchants might also want to emulate the aristocracy in this manner) but if called to war most other citizens typically relied rely on local authorities like guilds or their parish to both supply arms and run drills. While no two cities had identical institutions (some were more warlike and held regular tournaments and competitions in which citizens were encouraged to test their martial skills, others much less so) there were indeed instances where urban militias with varying degrees of equipment and training took to the field. This, for example, is one of several factors that explains the poor performance of Italian city-states against non-Italian forces which typically were more seasoned and well-equipped (even when numerically inferior, more disciplined foreign troops generally got the better of Italian urban militias). However, other community militias could instead be highly effective and even sought-after to bolster the ranks of medieval armies, like those of Burgundy or Switzerland.

This answer by u/Rittermeister, and this other answer by u/MI13 might interest you. You can also read more in the FAQ section.