Firstly, field battles would only make up a small percentage of the fighting in a war. Most of it would be done in sieges and assaults on cities. Let's face it, despite being fascinating and exciting, they were a huge and risky gamble of supplies and troops. You could deal the same amount of damage with fewer men and supplies/equipment, when defending from behind a wall.

When field battles did happen, they were more of a game of morale than anything else. The first army to break and rout, despite its size, would lose the battle (unless they were able to regroup), and then was when most of the casualties happened. The victorious army would send, preferably, fast units - mostly light cavalry - to cause as much damage as possible on the retreating army, be it by capturing or killing. Unless one army was surrounded - like the Romans at Cannae (where most of the men fighting were either killed or captured) - breaking morale and routing was the most common means to win a battle. And that's logical because people don't want to die and, let's face it, they were a valuable asset to their leaders, so winning a battle with the least casualties possibly was the objective.

Here's the example of the famous battle of Gaugamela (331 BC; Macedons vs Persians):

The Macedonians were outnumbered:

The whole army of Darius was said to contain 40,000 cavalry, 1,000,000 infantry, and 200 scythe-bearing chariots. (Arrian's Anabasis 3.8)

Arrian's estimate on Persian numbers are thought to be largely exaggerated.

The whole of Alexander’s army numbered 7,000 cavalry and about 40,000 infantry. (Arrian's Anabasis 3.12)

Despite the disadvantage, Alexander, by striking at a vulnerable spot was able to generate chaos among the Persian ranks:

As soon as Darius began to set his whole phalanx in motion, Alexander ordered Aretes to attack those who were riding completely round his right wing; and up to that time he was himself leading his men in column. But when the Persians had made a break in the front line of their army, in consequence of the cavalry sallying forth to assist those who were surrounding the right wing, Alexander wheeled round towards the gap, and forming a wedge as it were of the Companion cavalry and of the part of the phalanx which was posted here, he led them with a quick charge and loud battle-cry straight towards Darius himself. For a short time there ensued a hand-to-hand fight; but when the Macedonian cavalry, commanded by Alexander himself, pressed on vigorously, thrusting themselves against the Persians and striking their faces with their spears, and when the Macedonian phalanx in dense array and bristling with long pikes had also made an attack upon them, all things together appeared full of terror to Darius, who had already long been in a state of fear, so that he was the first to turn and flee. The Persians also who were riding round the wing were seized with alarm when Aretes made a vigorous attack upon them. In this quarter indeed the Persians took to speedy flight; and the Macedonians followed up the fugitives and slaughtered them. (Arrian's Anabasis 3.14)

Although the battle had not ended by this time, you can have an idea of how morale and attacking retreating enemies played an important role on ancient battles.

Note - the excerpts of Arrian's accounts are from this site.

Edit: typo