Well I can't speak for all medieval battles as that covers a huge area but can answer for atleaat the Battle of Agincourt. The battle began with the French army following the English for a few days until king Henry V decided that he had to fight. The battle began with both sides staring at rah other until Henry initiated things with his archers. The actual major engagement of the battle lasted only an hour or two but it's hard to know for sure as medieval historians rarely recorded specific timelines. There were a few smaller skirmishes later through the day but there was no action the second day. The battle ended with the French deciding to withdraw and Henry did not follow. Also both sides had heralds that watched the battle in a neutral position. At the end of the battle the French heralds agreed it was an English victory. They also settled on the name of the battle then. The French had a rather orderly retreat after the battle and Henry had no motivation to pursue the army. English casualties were rather limited as most wounds inflicted would have been lacerations from swords rather than puncture wounds like the French suffered. Because of this the majority of English wounded would survive the battle. The French wounded though suffered many puncture and stab wounds from English arrows. These had a much higher rate of infection. French wounded were also left on the field without medical aid and those that could not support themselves were likely to bleed out. As for the bodies lords and other high ranking soldiers might be given some kind of burial but for the majority of soldiers their bodies would end up in a mass grave. Highborn soldiers were much more often captures for a ransom rather than killed. Hope this helps answer your question.