The answer to that questions depends on who, when and where.
Generally speaking in the early modern era (1600+) training was in the hands of the unit commander, and it could vary considerably between units.
As time progressed training became more standardized. By the Napoleonic era most training regimes were standardized across the army. Although reserve units could have varying levels of training. The unit commander’s focus and dedication also varied with some units being more focused on marching and uniforms and other units spending more time on martial training.
Officers generally paid for their own sword training and went to fencing schools. Soldiers followed drills published in books with a smaller set of standardized moves.