Armies can be as simple as a mob or raiding party with little to no leadership, or a rigidly hierarchal organization with clearly defined roles for all members. According to the Saxon Laws of Ine an army or here consisted of 35 or more men.
Professional standing armies, such as the Roman legion or the modern army, were comparitively rare in period. While medieval armies were made of warriors who trained their whole lives to fight, unit discipline and organization tended to be limited to personal bonds of fealty. In addition, many feudal armies had an extremely limited term of service, typically forty days.
Most armies are headed by a single commanding officer. Authority can be delegated to lieutenants, who are in charge of individual divisions or units of the army. In large fighting forces (like what would be found at an SCA war), there might be more than one level of leadership, with orders going from the general to a lieutenant, to a sergeant, to the individual soldiers. This is referred to as the chain of command.
Historically, it was generally agreed that the better the leadership of an army is, and the more responsive the soldiers on the field are to that leadership, the better an army will perform on the field. For this reason, generals tend to be accomplished fighers, who studied tactics and military theory.
Training and discipline
As with any hierarchical organization, if individuals in the organization do not accept their station the performance of the whole unit will suffer. For this reason, most modern professional armies undergo extensive training to the aim of instilling discipline, training in specific roles, and an esprit d'corps.
Armies in the SCA
Most SCA armies tend to be fairly well-trained (better than many armies in period, at least, since SCA fighters have extensive practice with their weapons). SCA fighters also have more in common with medieval warriors that modern soldiers do, since SCA fighters are volunteers and largely lack the discipline of a professional soldier.
Armies in the SCA are usually raised by Kingdom or Principalities, although some are raised by Baronies or Shires. Kingdom armies tend to be made of units comprised of forces fighting by barony shire or canton, although large households often fight as discrete units.