My area of expertise is a little early to answer your question properly, and I hope u/HatMaster12 will make an appearance. However, making the unfounded assumption that some of this may not have been so different between Classical Greece and Late Antiquity, here goes:

The main point to bear in mind about ancient armies is that they were usually very large bodies of men followed by very large baggage trains and throngs of camp followers. They moved very slowly and usually along very predictable routes. It was difficult to hide an army on the move; it either demanded supplies or caused widespread destruction, it raised clouds of dust as it marched, it created a field of campfires at night, and so on. It was rare, therefore, for defenders to be taken by surprise. Only an army that moved unusually quickly, by unexpected routes, or at night, might be able to reach places that were not prepared against it. If the defender had border forts or watchtowers on his borders, or made use of scouts, it would be all but impossible for an enemy army to approach undetected.

Where to send the defending army would then be a matter of either predicting or shadowing the enemy's moves. Once the two armies were in sight of one another, they would encamp and prepare for battle. In Classical Greece, the side that reached favourable ground first might form up and dare the enemy to attack; if this failed, they might come down to fight it out on level ground. The Greeks normally tried to attack by surprise in terrain where they had the advantage; however, if there were no more opportunities for this, the battle would appear almost prearranged, in the sense that both sides knew exactly what was going to happen and where. The defender would simply block the attacker's path and play a game of battle chicken. There are occasions where armies formed up for battle and waited, day after day, without actually coming to blows.

As for the aftermath: when one side broke and fled, at least in Classical Greece, the other side would pursue them and slaughter them with impunity. This was open season. The entire point of their battle was to reach a point where the enemy ceased to resist, so that they could be killed at will. If light infantry and cavalry were present, the routed enemy would be pursued for miles, often until nightfall made it impossible to go on. Hundreds, sometimes thousands would die.

The important thing here, though, is that the camp and the battle line were usually not in the same place. Armies marched out from their camp - leaving behind their supplies, their loot, their servants and hangers-on - in order to do battle somewhere nearby. Sometimes they would leave the oldest warriors behind to guard the camp. The consequence of this is that when they broke, they tended to flee back towards their camp. Those who were defending their territory would often head for the protection of a nearby friendly settlement or city wall. At that point they normally regained some of their order and control, and a wise enemy would break off the pursuit. Therefore, unless the camp had previously fallen into the hands of the enemy and looted (which horsemen were particularly prone to doing instead of actually supporting the battle line), the defeated would normally be able to return to their supplies and continue to exist as before, except beaten and with depleted numbers.

If the camp had been looted, or if the enemy did continue the pursuit once the defeated had reached their camp, then indeed the beaten side would be in very serious trouble. They would either be wiped out by the victors or they would have to find a friendly polity nearby to provide them with food. There's one poignant scene in Greek history where an army whose baggage had been looted had to resort to using captured enemy shields as firewood to make it through the cold night.

The winners would not generally care about their camp at this point, as the assumption was that no organised enemy forces remained to threaten it. They would pursue until they had had their fill, and then make their way back to their own camp.

The key point of all this is that the movement of an army on the march and its movement in battle were not of the same nature. Ancient armies needed their baggage and camp followers to function. The fighting men that formed up and fought the battle were only a part of the army as a whole, and once they were done fighting they had to return to camp so that "the army" could advance or retreat. An army on campaign could march for days; in pitched battle, the victors might pursue for several hours, but then they simply returned to camp.