Following the successful end of a conflict, how would soldiers levied from the general population go about returning home? Was this process typically disorganized, or was there formal ceremony behind the dissolution?
I'll give you a short answer now, but I may go into more detail later. I'm gonna assume you're asking about the high and late middle ages here, please correct me if I'm wrong. While knights and retainers could be considered a permanent military force in most of Europe, the majority of armies were composed of mercenaries, levied troops or militia. These were respectively professional soldiers, trained civilians (conscripted or voluntary) and the citizens of a town raised in arms to defend their land.
In general, after an armed conflict was done the armies returned to their land, any due wages were paid and the civilian troops returned to their homes in large groups, since many of them could be raised from the same town. They retained their arms and armor, since they were the ones to provide it in the first place. Mercenary troops simply reunited with their commanders and went on to find further employment.
Of course, there was always the possibility that some soldiers banded together to form robber gangs, or even small armies. This was particularly common during and after the Hundred Years War, where thousands of mercenaries, men at arms and even knights formed the infamous Free Companies, which would later travel to Italy and work as mercenaries for the wealthy city states.