We tend to think of medieval houses as built of stone because most obvious surviving medieval buildings are stone. But these buildings are churches and castles for the most part, not regular people's houses.
Wood was the most common building material in the Middle Ages, as it still is in the modern US, because it was fairly cheap and easy to work. The earliest castles were built with wooden palisades, and palaces were largely built of wood. In Scandinavia, churches too were often built of wood.
But in the twelfth century wood started becoming scarce. As the population grew, forests were cut down for new crop land. Efforts were made to protect the remaining forests, for hunting or for pasturing pigs. So big beams became hard to find.
Ordinary people's houses were built mostly of what is called wattle and daub, small pieces of wood providing a framework, filled in with a combination of straw, twigs, mud, and maybe plaster (sometimes dung). If one thinks of what we now call half timber, wattle and daub was a rougher version--most existing half timber structures were built in the fifteenth century or later. If the whole thing was whitewashed, it wouldn't look too bad.
Wattle and daub was not strong enough to support a multi-story house, so most medieval houses would be two stories high at most. The floor would be dirt; conscientious housekeepers would try to keep it (vaguely) clean by constant sweeping, which meant that the floor might end up several inches lower than the ground outside.
If there were nearby marshes, thatch (made from reeds) was a popular choice for the roof. A well made thatch roof will last for over thirty years, although nowadays thatchers say that acid rain has resulted in weaker, less long-lasting reeds. The problem with thatch is that it will burn, so in towns those constructing houses were encouraged to use tiles or slates instead.
Starting in the twelfth century, a few wealthy townspeople might build a house in stone. Such a house was far more expensive but much longer lasting. It could also be built higher. Such a house might have a flagstone or tile floor, rather than dirt.
In the late Middle Ages, more and more people started building in stone. One of the effects of the devastating Black Death of the fourteenth and fifteenth centuries was that the population was severely reduced, leaving more wealth for the survivors. Most European stone villages took the form they have now between the fifteenth and seventeenth centuries, although there are still some twelfth-century structures mixed in.
In the country, the barn with its animals was usually built immediately adjacent to the farmhouse (see more here). Barns became stone at the same time as the farmhouses. A medieval stone barn was built as a series of long, narrow open areas with stone walls in between, which made it easy to span the open areas with short boards, for the upper story (hay or grain storage).
Most medieval houses did not have fireplaces. Instead they had a fire pit, the smoke from which made its way out through small holes near the eaves. Fireplaces really only came in during the thirteenth century. They were more expensive and much less efficient in heating the place, so they generally were found only in castles or palaces.