During the middle ages bows were manufactured by bowyers, a craft guild which still exists today. The guild operated much like any other at the time, apprenticing boys and training them over a period of roughly seven years. The guild was and still is, a guarantee of quality for the trade of bow making.
Today bows can be made from all sorts of materials, even without any wood at all, which would seem fantastical to a medieval bowyer. Modern bowyers have incredibly efficient glues. This adhesive technology allows them to create laminated bows, with different types of wood selected for strength, flexibility and often it seems just for good looks. No such luxury for the medieval bowyer, he had no choice other than to build 'self' bows, made from a single stave of wood.
The premium wood for bow making in the middle ages was yew, and is still considered the best bow wood today by traditional bow makers. Ash, and other 'mean' woods, such as wych elm were also used, but yew was prized for its strength and flexibility provided by the tree's heart and sap wood. The photograph below clearly shows the definition between the heart and sap on a piece of yew. A piece of ash is also shown, popular too for making arrow shafts.