The middle ages span a millennium and during that period there was significant diversity in taxation and political structures across Europe. You may want to post the question again, narrowing the time and space you are interested in.

In the eleventh century, for example, you had the Byzantine Empire that still used (very successfully) the land-based taxation system of the Roman Empire, and was able to use the steady, fairly reliable income to keep a standing army and maintain infrastructure. You would have a hierarchy with the emperor at the top and local government administrators collecting taxes at the bottom. On the other end, you have western Europe where taxation was an occasional thing only activated at times of war and crusades. Kings tended to have relatively weak power. In France, for example, the king would nominally rule over all of France, but in reality would only control a small area centered around Paris. The rest of the country was in the hands of regional lords, who nominally ruled over their region but, again, usually only had real power over a small portion of it. Power was mostly in the hands of local barons, who controlled the local economy and justice system. Two centuries later, after the Albigensian crusade in the south and wars with England in the west, power in France was more centralized and the local level had been replaced with bureaucrats appointed by the crown. By then taxation was becoming a more regular occurrence in France.