The general trend i would say is that more dedicated, large institutions began to emerge as you get into the late medieval period and reconnaissance. One of the most famous examples was the Marxbrüder, Brotherhood of St. Mark, who were considered the finest school for training in the use of the Zweihänder in the Holy Roman Empire. Graduates from the school being the only ones who could officially call themselves masters could expect to see double pay fighting in the ranks of Landsknecht mercenary companies. Other institutions include the Company of Maisters of the Science of Defence, the foremost English fencing school (note that at this time fencing did not refer to the sport of fencing but combat arts in general). In Italy the University of University of Bologna included one of the most famous sword schools of Italy.

Earlier on given that military training and power was typically less centralised individuals would be more likely to simply be trained on a more local basis. Archery would be learned at a local butts from relatives and/or perhaps an experienced local archer who didn't mind taking a little time out their day. For those who were dedicated soldiers likewise a veteran might well tutor you in combat.