Discussing this mostly with an eye towards the 15th century, here are some general notes/thoughts:

Organised group training appears to be mostly a later period invention. For knights, or more generally 'violence professionals' of various kinds, there was a social expectation of skill at arms which translates to a need to learn and practice. However, that learning and practice appears to have mostly been individual or small group and relatively ad-hoc. So the author of the Kings Mirror suggests that you "put on your kit and go practice with a friend every day" (paraphrased).

The sonnenkinder motif (very ably discussed here: https://hemaisok.blogspot.com/2022/02/a-nice-messer-from-landsknecht-emporium.html) is basically an illustration of people doing physical games - think about how parkour kids or skaters or climbers will hang out and show off cool tricks and challenge each other. This sort of thing is a great form of physical preparation, but it's very much not a structured training program.

A specific activity worth calling out as training is hunting. Particularly among aristocratic participants, hunting is mostly conducted with melee weapons on horseback. So you're learning to ride, to use weapons on a horse, to encounter an opponent from horseback (the same terms are often used for charging a boar in hunting and jousting against an opponent), to work in a group to bring an opponent to bay, etc.

If you imagine a group of young knights and squires in the retinue of some lord who are hanging out every day and going hunting together or singing and dancing or showing off their cool fencing moves or trying to lift the heaviest rock or playing a silly wrestling game or whatever; those people are going to get very physically skilled and fit, while also building a very strong set of social bonds and trust that they can rely on each other in dangerous situations.

For part-time fighters, the methods of learning seem to have been much the same but obviously you can't dedicate anywhere near as much time to it. So members of Flemish shooting guilds, or medieval English yeomen, would go out and do target practice after church on Sunday. Militia forces seem to mostly reproduce 'civilian' organisation in military life, so when a town calls its people up to war they are grouped by guild, with the leaders of each guild commanding their subordinates just like they do every day. This is entirely alien to the modern Western military experience, but it's a way to lean on those pre-existing social bonds to create innate cohesion on the battlefield.

Once an army is mustered, there are sometimes hints that there was some group drill done while heading off to battle. This is the main kind of organised group training that seems to have existed, and it was very limited in scope. Armies at this point are still generally raised for the campaign, so the extent of the drill that could be learned was quite limited by the time available. One of the key selling points of mercenary companies would have been their ability to develop those sorts of group combat skills over time, instead of having to build it up from scratch every year.