From Barbara Hanawalt's The Ties That Bound, a wonderful study on medieval peasant households and life in general:

"The general layout of house interiors on the ground floor is most clearly seen in the case of a Devonshire farmstead, Dinna Clerks, which burned, burying its contents. This excavation showed a central granite hearth in the main room and a wattle-and-daub hood over it that channeled smoke through the roof. Four small cooking pots were found, a green glazed jug, and a cooking pot buried to its rim in the floor. The purpose of this latter pot is not known, but it may have been used for water. In the inner room of the house, which served as a storage or sleeping room, there was a cistern." (39)

Worth noting that this is an example from late medieval England, so don't take it as necessarily typical of everyone in Europe. That said, these cottages were very simple, and they didn't exactly have kitchens like we're used to thinking of them in houses. The most basic one-room cottages had that hearth in the middle, and that was the center of activity. Bigger homes owned by wealthier peasants might have extra rooms or even more hearths (one peasant is noted to have started a fire at a relative's house by trying to take coals from one hearth to the other). Postholes have been found near the hearths, presumably where they stuck spits to hold the pots, and they just cooked out of pots and pans over their hearths. There are a lot of records of peasants getting hurt from those open hearths, too. Overnight, they'd cover the hearth with a big metal dome with holes in it to let it keep them warm while running a slightly lower risk of burning everyone in the middle of the night. Some houses had fire pits in the walls for baking, but proper internal ovens were uncommon in England--they were all over central Europe, though. As far as utensils, cottagers have inventories including things like tablecloths and metal knives to complement other cookware, as well as relatively high-quality whetstones with decorative patterns, suggesting peasants invested a good bit in women's work around the house. For wealthier peasants, you might also have wooden bowls, forks, and spoons for general use, kept in hutches and small cupboards, and these wealthier types might also sport benches for their tables. Stools were rare. Silver spoons are present in some houses, but kept under lock and key in a chest, since break-ins were a concern.

Source: Barbara Hanawalt, The Ties That Bound, Chapters 4 and 5, also includes a much broader overview of the peasant household.