My own knowledge on this is fairly limited, from looking at Scandinavian history it seems as if, from about the 15th century, there is an increase in participation in armies. How did this occur elsewhere in Europe and how big did these European armies get?
In the Medieval period, most of the European kingdoms had the feudal system. In this system every king and every one of his vassals had their forces, and when war came, the vassals would supply fighting men to the king's army. Countries didn't have standing armies.
After the Black death, feudal rulers started to lose their grip over their subjects, and the feudal system slowly declined. In it's stead, more centralized kingdoms emerged. In the mid 15th century, kingdoms slowly started to form standing armies. These were permanent professional armies consisted of trained soldiers that would not disband in times of peace. The first standing army in Western Europe was established by the Charles VII of France in 1445, tho I don't know the size of that army. One other notable standing army was the Black Army of Hungary (Fekete Sereg), established by Matthias Corvinus in 1458. The size of this army is approximated around 28000 soldiers.