If you want to store food the right way in Going Medieval, you will need to build a storage space for it. To do this you will need to open the zone menu and then click the default stockpile option under the zone tab.
Once clicked you will be able to highlight an area to store your food in by selecting the default stockpile option. However, you should not just select any old patch of land.
The reason why is that food will perish quickly in the game, so you will need to build your food storage underground.
Building your food storage space underground will allow you to keep it fresh and cool. That said, to make an underground food storage space, you will first need to clear out a space by hitting N on your keyboard, which is the mine key.
After this, highlight a small area to have your settlers begin digging the area, and when they finish, highlight the area again with the default stockpile key.
Also, make sure to place some stairs and close the storage space up with walls, floors, and a roof as well, or your food will not be kept fresh basement stockpile.
You can also change the way you make food to help it last longer by either building distillers to make vinegar or a smoker to make smoked meat.