In the traditional way of conducting war there were two classes - nobles and commoners. Nobles fought on chariots, on horses, or sometimes on foot, but always fully armed and trained. They were brave, but fought individually, for honor and loot. The commoners were poorly armed and occupied themselves mostly by shooting arrows etc. They were used as "filler", to stop the enemy nobles from free movement on the field. Real killing was done by elite.
The fighting, except for massed chariot charges, was done in spurts. (And cavalry also charged and then retreated). Two crowds stood facing one another and shooting arrows etc. From time to time a hero would jump forward, kill somebody and retreat into his own crowd. All were afraid of being attacked from the back, and so always had to retreat. You can see that kind of fighting on football stadiums.
The visible sign of hoplite revolution was moving the handle on the shield from the centre to the rim. This way, the shield covered mostly the neighbour, and the hoplite couldn't fight alone at all. He had to fight in a line which moved all at once.
Herodotus, Battle of Plataea
"For the Persians had made a rampart of their wicker shields, and shot from behind them sUch clouds of arrows, that the Spartans were sorely distressed. The victims continued unpropitious; till at last Pausanias raised his eyes to the Heraeum of the Plataeans, and calling the goddess to his aid, besought her not to disappoint the hopes of the Greeks.
As he offered his prayer, the Tegeans, advancing before the rest, rushed forward against the enemy; and the Lacedaemonians, who had obtained favourable omens the moment that Pausanias prayed, at length, after their long delay, advanced to the attack; while the Persians, on their side, left shooting, and prepared to meet them. And first the combat was at the wicker shields. Afterwards, when these were swept down, a fierce contest took Place by the side of the temple of Ceres, which lasted long, and ended in a hand-to-hand struggle. The barbarians many times seized hold of the Greek spears and brake them; for in boldness and warlike spirit the Persians were not a whit inferior to the Greeks; but they were without bucklers, untrained, and far below the enemy in respect of skill in arms. Sometimes singly, sometimes in bodies of ten, now fewer and now more in number, they dashed upon the Spartan ranks, and so perished.
The fight went most against the Greeks, where Mardonius, mounted upon a white horse, and surrounded by the bravest of all the Persians, the thousand picked men, fought in person. So long as Mardonius was alive, this body resisted all attacks, and, while they defended their own lives, struck down no small number of Spartans; but after Mardonius fell, and the troops with him, which were the main strength of the army, perished, the remainder yielded to the Lacedaemonians, and took to flight."
Some descriptions of ancient and modern kind of war:
What Spartans thought about those that left their rank for any reason:
(Herodotus, battle of Plataea)
"The bravest man by far on that day was, in my judgment, Aristodemus - the same who alone escaped from the slaughter of the three hundred at Thermopylae, and who on that account had endured disgrace and reproach: next to him were Posidonius, Philocyon, and Amompharetus the Spartan. The Spartans, however, who took part in the fight, when the question of "who had distinguished himself most," came to be talked over among them, decided - "that Aristodemus, who, on account of the blame which attached to him, had manifestly courted death, and had therefore left his place in the line and behaved like a madman, had done of a truth very notable deeds; but that Posidonius, who, with no such desire to lose his life, had quitted himself no less gallantly, was by so much a braver man than he." Perchance, however, it was envy that made them speak after this sort. Of those whom I have named above as slain in this battle, all, save and except Aristodemus, received public honours: Aristodemus alone had no honours, because he courted death for the reason which I have mentioned."