/u/Iphikrates has given a good answer on a similar question here. While neither Iphikrates nor myself are experts of medieval warfare, the mechanics of massed infantry combat didn't change much until the invention of firearms. Indeed, newer understandings of how ancient warfare worked (Goldsworthy 1996; Sabin 2000) is heavily based upon the work of John Keegan on Agincourt (1976). So I'll talk a little about ancient warfare, and while someone who knows more about the medieval period can probably give you a more period-specific answer, I don't think battles in the medieval period would generally have been more chaotic, confusing, or organised than they were in the classical period between great states. In fact, the smaller numbers involved in many medieval battles might have made them less confusing.
Battles were "well organised" in that infantry usually fought in formations and tended to hold their formations as best they could. While it has been argued in recent years that any massed infantry battle would see a number of "natural fighters" facing off in the front lines while less keen soldiers would make up the rear ranks, I subscribe more to the view that the front ranks of infantry formations were a combination of good fighters but also the youngest men, especially in the Roman context. As discussed in the above link, infantry battles did not generally tend to devolve into chaotic melees, but were more tentative affairs that involved intense formation fighting (often with polearms in the medieval period) and periods of rest as groups of men separated slightly for a rest, or one side gave ground and the other side closed the gap or let it stay open to give themselves rest.
However, in the final stages of pitched battle, it became far more chaotic. Flank/rear charges (generally by cavalry), decisive infantry charges (where one side is psychologically far superior to the other), poor morale or fatigue are the main causes for a total collapse in the rough fighting "lines" that infantry battle occurred in. Once this collapse occurred, battle would become far more chaotic. The bulk of the defeated troops would begin to retreat, some would throw their gear down and run, and some would fight as they had no choice, while a remarkable minority (eg. Sacred Band of Thebes at Chaeronea) would hold their ground and fight at full effectiveness. As the infantry formations of the losing side broke down, the winning side would also lose formation cohesion as the men began to engage in pursuit and slaughter of the losers. At this point in battle, individual duels would occur, the lines would become confused, and it might become harder to tell friend from foe. But at this point, a battle was generally decided.
Other factors would contribute to the chaos of pitched battle, even where the infantry broadly held their formations. Factors such as the great clamour of battle and the dust that might be kicked up, limiting sight to perhaps a few metres, would increase confusion. Livy's account of Trasimene (22.4-6, read here ) is an excellent literary description of how confusing a pitched battle could be for soldiers. I'll quote a choice section:
When the Carthaginian saw his object achieved and had his enemy shut in between the lake and the hills with his forces surrounding them, he gave the signal for all to make a simultaneous attack, and they charged straight down upon the point nearest to them. The affair was all the more sudden and unexpected to the Romans because a fog which had risen from the lake was denser on the plain than on the heights; the bodies of the enemy on the various hills could see each other well enough, and it was all the easier for them to charge all at the same time. The shout of battle rose round the Romans before they could see clearly from whence it came, or became aware that they were surrounded. Fighting began in front and flank before they could form line or get their weapons ready or draw their swords...But such was the uproar and confusion that neither counsel nor command could be heard, and so far was the soldier from recognising his standard or his company or his place in the rank, that he had hardly sufficient presence of mind to get hold of his weapons and make them available for use, and some who found them a burden rather than a protection were overtaken by the enemy. In such a thick fog ears were of more use than eyes; the men turned their gaze in every direction as they heard the groans of the wounded and the blows on shield or breastplate, and the mingled shouts of triumph and cries of panic. Some who tried to fly ran into a dense body of combatants and could get no further; others who were returning to the fray were swept away by a rush of fugitives. At last, when ineffective charges had been made in every direction and they found themselves completely hemmed in, by the lake and the hills on either side, and by the enemy in front and rear, it became clear to every man that his only hope of safety lay in his own right hand and his sword. Then each began to depend upon himself for guidance and encouragement, and the fighting began afresh, not the orderly battle with its three divisions of principes, hastati, and triarii, where the fighting line is in front of the standards and the rest of the army behind, and where each soldier is in his own legion and cohort and maniple. Chance massed them together, each man took his place in front or rear as his courage prompted him...
So basically, one shouldn't generalise to describe all battles: each one was different, with peculiar characteristics and unique context. Some battles would have been well organised and easily controlled by commanders who had carefully chosen their ground, while small changes in fortune or the morale of the troops (surprise attacks, the wounding of significant individuals) could change the course of a battle and cause panic to set in. Once panic set in, a battle could collapse into chaos and become very confusing indeed, but the side doing the panicking would be the losers.
Reply from /u/400-Rabbits about a very similar topic a few years ago: