Italian Knight c. 1400 C.E.
Logistically Medieval armies of the 12th and 13th century tended to live off the land which made them veritable plagues of locusts to the locals who where unfortunate enough to be where the armies were. Crop surpluses were very low. Generally yields of crops were on the order of 1 to 3 to 1 to 6, in some cases it was a very bad 1 to 2. the above figures are the ratio of planted grain to yield. I.E. for every 1 grain planted you got 3 or more grains. This meant that a sizable portion of the harvest had to be saved as seed grain for the next planting. Of course the peasants also had taxes to pay and dues owing to their lords. Both of which were frequently quite substantial. This made living fairly precarious. Add an army marching through to the mix and life became vastly more difficult if not impossible. Peasants usually viewed armies as a curse and punishment from heaven, even if the army was their army. Areas through which armies went through were usually swiftly devastated. Added to this Peasants were frequently forcibly conscripted to provide labour services to armies, men forcibly billeted on them. Not surprisingly regions in which armies appeared were often depopulated as people fled, and often took decades to recover.
Further adding to the problem was that Medieval governments were almost always chronically short of cash to pay their troops. The result is that the armies would squeeze the locals not just for supplies but for cash. In theory medieval armies raised by the feudal system didn't have to be paid, but were the responsibility of the feudal underlings to pay costs. The actuality was far different; large amounts of cash were needed in a chronically cash poor society. Many of the Lords in Medieval Europe had lots of vassals but little cash and many vassals lacked the financial wherewithal to go campaigning without a monetary subsidy. For example it appears that many vassals had a very hard time simply getting together the necessary equipment. Say a suit of armour, which was by then standard equipment was spectacularly expensive. (I've read various estimates of the cost in terms of an average peasant’s yearly "wage", but the lowest I've heard is something like 50-100 years worth for a full suit of mail. Plate armour was even more expensive, to say nothing of a sword, a trained war horse etc.
A large component of medieval armies, at least of the nobility, was second and third etc., sons seeking their fortune because the system of inheritance in which the eldest son got practically all of it left them out.
Some Medieval generals and leaders did on occasion try to lay in supplies for a campaign and provide logistic support. These efforts were not common, mainly because medieval roads were very bad and therefore transportation costs were very high and has mentioned above medieval governments were cash poor. Sometimes medieval governments tried to get enough cash together so they could buy supplies and leave their peasants alone. But all such efforts were short lived and medieval armies soon went back to what amounted to pillaging the countryside.
If medieval armies were curses to their own people, they were horrors to their enemies. The typical medieval military strategy while on campaign was the chevauchee. This involved going through enemy territory and pillaging everything within reach, burning villages, stealing everything that could be taken and often killing everyone not worth a good ransom. The rules of chivalry were generally held to only apply to relations between the Nobility. Pitched battles were actually fairly rare, but there was generally much skirmishing, pillaging, looting and myriad atrocities against enemy civilians.
Although most medieval states could call out, in theory, large numbers of peasant militia. Those men were generally useless in an army and therefore not frequently used. When they were used if they were on the losing side they were frequently butchered en-mass. Not worth good ransoms you see. They were ill trained and very ill equipped. Good military equipment was very expensive. Medieval states usually preferred to exact taxes from the peasantry to hire soldiers who could fight well.
As for garrisons. Well medieval armies being poorly paid, if at all, would get their money from the area they were protecting. In the Hundred Years War this practice was called the patis. It was basically a vast protection racket. In which the garrison would levy contributions on the locals and threaten fire and sword if they weren’t paid. And of course inflict fire and sword if they were in fact not paid. To this was also added exactions for supplies and billeting. The fact is even the small permanent garrisons that the English had in France during the Hundred Years War terrorized the locals to such an extent that the population of the areas garrisoned fell significantly even in areas far from the fighting. Also even when garrisons were paid, there was lots of money to be got squeezing the locals and lots of people made oodles of cash.
Governments had a very hard time paying for armies even temporarily; a garrison represented a terrible drain on finances so that a garrison system on a border was during the 12th and 14th century a pipe dream extravagance. The English during the Hundred Years war were able to have garrisons only because of the patis and a systematic policy of exploitation. As it was their official garrisons were small. There was however also the plague of unpaid soldiers who made do with pillaging the locals, and extracting patis freelance and where called back into official service when necessary.
In the late 14th century the French king Charles V was able to create something like a standing army of c. 3-5 thousand men only by straining every financial expedient to the max and taxing his subjects ruthlessly. Even so the effort eventually proved too much. This was in a nation of c. 12-15 million at the time. In the 15th century Charles VII of France was able through extensive financial and other reforms to create a standing army of c. 8,000 men, based on the same population as under Charles V. More importantly, at least from the point of view of a peasant, (the overwhelming majority of the population), he was able to insure that it was paid regularly and better yet much more disciplined so it didn't go off and pillage and devastate the people it was allegedly protecting at the drop of a hat. Charles VII was even able to organize a commissariat that if not terribly effective was effective enough to reduce the need to live off the country and just as important arrange so that money was available to buy supplies. The result was an army that was less destructive than previous armies.
McGlynn, Sean, By Fire and Sword, Phoenix, London, 2008.
Seward, Desmond, Henry V as Warlord, Penguin Books, London, 1987 and The Hundred Years War, Atheneum, London, 1978.
Oman, Charles, The Art of War in the Middle Ages, Blackwell, Oxford, 1885.
Fuller, J.F.C., A Military History of the Western World, v. 1, Da Capo, New York, 1954.
Barker, Juliet, Conquest, Little Brown, London, 2009.