Military thinkers of the Hellenistic and Roman Imperial periods (c. 300 BC - AD 300) are pretty clear on how orders should be communicated to the troops. Generals should use trumpet signals for advance, retreat, manoeuvre, and changes of formation. They should also use vocal commands, which should be transmitted by lower-ranking officers until the men carry them out. Officers in charge of smaller units should be able to control their men by shouting words of command that their troops have been drilled to understand and obey instantly.
There's just one problem with all this: it requires discipline and training. Men need to be silent to hear their orders, and carefully drilled to carry them out. They also need to have familiarised themselves with a range of different signals. Professional armies like those of the Hellenistic kingdoms or the Roman Empire could meet these requirements. The militias of Classical Greece, however, could not. Greek armies were composed of citizens, called up for a particular conflict and thrown into battle with zero preparation. Their armies lacked an elaborate officer hierarchy that would allow the smooth transmission of orders, and didn't have the training to recognise any complex signals or words of command. They had trumpets, but as Peter Krentz noted when he gathered evidence for their use, the Classical Greeks seem to have recognised only two signals - the charge and the retreat.^1
The result is that Classical Greek armies simply couldn't be given orders once battle had begun. Whatever they needed to do in the battle had to be made clear in advance. At Plataia in 479 BC, when the largest Greek army ever gathered was preparing to fight the Persians, their plan was simply to line up and fight whoever they found in front of them. At one point the Spartans on the right wing sent a messenger on horseback to the Athenians on the left, ordering them to come and support the right, but the Athenians found themselves under attack before they could complete the manoeuvre, and had to fight where they were. There's no other case where such an order was even attempted mid-battle. The only troops that could carry out complex manoeuvres were smaller units, usually under the direct command of the general. There is one example of a fire signal from a tower in a city wall being used to give orders to friendly troops during a battle, but this could only work if there was a suitably high place to give the signal from, and again, it had to be agreed in advance.
The Spartans themselves were the exception to the rule. The Athenian historian Thucydides describes the way they deployed for battle at Mantineia in 418 BC, and his account and careful naming of all the officers betrays his awe at their level of organisation and discipline:
There was little time for preparation, as they instantly and hastily fell into their ranks, Agis, their king, directing everything, agreeably to the law. For when a Spartan king is in the field, all commands proceed from him: he gives the word to the polemarchs; they to the lochagoi; these to the pentekostyes; these again to the enomotarchoi, and these last to the enomotiai. In short, all orders required pass in the same way and quickly reach the troops; as almost the whole Spartan army, save for a small part, consists of leaders leading leaders, and the care of what is to be done falls upon many.
-- Thucydides 5.66.2-4
The Spartan method here is clear and simple. The king gives an order to the highest-ranking commanders; these pass it down to the ones below them; those to the ones below them, and so on until the commanders of the smallest units shout the command at their troops. Other Greeks could not copy this system, because their officer hierarchy stopped at the level of the lochagos, who typically commanded several hundred men and couldn't reach them all with the sound of his voice. The vocal relay mostly served the Spartans well, and they even used it when they commanded an army of many allied units:
And when they had been drawn up together in the positions which the Spartan leaders of the allies assigned to the several contingents, they passed the word along to follow the leading unit, and the Spartans led to the right (...)
-- Xenophon, Hellenika 4.2.19
Their ability to steer large numbers of troops in this way gave the Spartans an advantage in battle. The superior organisation of their infantry also helped to give their commanders more control over what happened on the battlefield. However, the weakness of the system is obvious: it relies on the smooth operation of the chain of command. If any link breaks, or if the men are simply too busy fighting to pass on an order, the Spartan army can't do anything more than any other Greek force. There was no system of command outside the phalanx, directing its movements from afar; there was only the king or polemarch, giving orders while fighting in the front rank. In the 370s BC, the Thebans worked out how Spartans could be defeated in battle:
They figured that if they conquered that part of the army which was around the king, all the rest of it would be easy to overcome.
-- Xenophon, Hellenika 6.4.12
Or, as a later source claims the Theban general Epameinondas put it:
If you crush the head of the snake, the rest of the body is powerless.
-- Polyainos, Stratagems 2.3.15
It wasn't until the rise of professional armies in the Hellenistic period that more reliable systems of command and control could be attempted.