It did depend a lot on the specific conditions. An army could often be able to collect quite a bit of food from the locals. Either hunting and gathering or pillaging/taxation of the local farmers. The problem with this is that it was unreliable and it often meant the army would spread around a lot and not move very fast. So a general would always want to provide enough supplies for their army as they marched, although some local resource gathering would usually be done anyway.
So the generals would set up supply lines from home to their army. Whenever they moved their army they would always have to tell the supply line so they could shift the supplies. As you could imagine this all depended heavily on allies. Both as a source of some supplies as needed but also to make sure nobody attacked these supply lines. It meant that armies could not march far into unfriendly territory. And passing for example a single castle without besieging it could easily cut the supply lines forcing a retreat. We have several examples of wars being lost due to lost alliances cutting the supplies. We also have stories of generals losing an army when they had to gather their own supplies and ended up getting picked off, deserting or fighting each other.
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