In respect to Napoleon, I would request you look at this previous answer I've given in the past which directly discusses Napoleon's command. If you have any other questions or follow ups about Napoleon and the Napoleonic Era, please ask and I will help to the best of my ability.

In the classical Greek armies, generals tended to lead from the front rank. Their job was to get their men to the enemy, choose when/where to fight the battle, to get their men motivated to fight (via the usual pre-battle speech), take the portents, and at that point their job was essentially done and they fought with their men. The result was after the battle started, they could not control the battle as they're too busy fighting.

I'm not as well read on command and control in the Hellenistic era. What I understand is that Alexander still fought directly in the battles, leading a unit of heavy cavalry. However his tactic was to delay his charge until his forces created an opening for him to exploit at which point he could burst through an enemy flank and wreak havoc. So there's a bit more sophistication but again, once Alexander was committed he was then effectively out of command and unable to control his army which would have to operate individually under their individual commanders.

The Romans however had a much more sophisticated command structure. Aside from all of the duties mentioned above, the Roman commander would start with a council where he would brief his officers with his battle plan. If his army was large enough he might assign command of groups of units (e.g. assign a legionary commander to lead all the units of the left wing). After the battle commenced, his job wasn't to fight but to observe and react. He usually stationed himself behind the first line of soldiers, and being mounted, he could see farther and move about the battle line quickly. This permitted him to rally failing units, summon reserves from the 2nd or 3rd lines, or note and later reward individual acts of bravery. This let the general actually command his army and react to changing conditions.

If you look at Caesar at the Sambre in 57 BCE, the Gauls caught his army setting up camp and the Romans had to quickly rush into a rough battle line. Caesar had to move about the battlefield issuing orders, sounding the horn to summon troops to their standards from their work parties. Then observing his right wing was in serious trouble, he rode there, dismounted and moved to the front line to personally rally the men and being issuing orders to the unit to push out their formation (they had been pushed in and were getting too cramped to properly fight). This rallied and invigorated his men and they were able to stand and eventually defeat the Gauls.

A reply to /u/thisfunnieguy

This is a good question, however if I may offer, you are asking about thousands of years' worth of how armies are led. Further, if you want to understand how armies are led, you have to understand how armies were raised, maintained, trained, and paid.

One approach to understanding the above is to take a grand tour through a broad time range, such that you can appreciate how things sort of evolve, by contrast, through the ages. For that I recommend Sir Edward Creasy's The Fifteen Most Decisive Battles of the World, all oldie but goodie from the late 19th century that you can buy for cheap free on Amazon Kindle or some other format. It has flourish, and embellishes the heroes, but it does go into some detail of how command and control are implemented.

If look at our post histories, /u/DonaldFDraper and I have gone back and forth on this a bit, around the early modern era (1500s-1800s), during which historians have identified the military revolution and state formation. Because as I said, you can't fully understand how armies are led without understanding how they are raised in the first place, and who owns them. I wrote a bit about this here and here. The means through which states raise and control armies evolved very rapidly. At the same time, the sizes of armies increased exponentially, which necessitated further sophisticated command and control systems. We also saw closer coordination between various units, showcased in the Tercio pike & shot system.

For this, the best papers are C. J. Rogers' Tactics and the face of battle from "European Warfare: 1350-1750" a collection of papers edited by Tallett and Trim (2010). The same collection has fantastic papers by David Parrott and Jan Glete which covers how states changed from the late medieval era in order to be able to raise the ever-larger armies of that era, based on gunpowder warfare. In particular, Parrott has written extensively on the development of a strong, professional officer corp in the 17th-18th centuries as an important epoch in the development of the modern military.

So this isn't a direct answer, rather a suggestion as to how to further explore the subject. And let's be honest here: I love this subject! :D

I'm a Marine combat veteran from Afghanistan, so I have an okay understanding of how generalship and battlefield command works in a modern military

Could you give a bit of insight on that front? My view (shaped from the medi/movies/etc) is that they don't do much up front? Is this accurate? If so, it would bring up an interesting question for me - at what point did generals shift from front line soldiers to rear to back at base? While I cannot comment on the names you've mentioned, generals in the Korean War were definitely in the thick of things. Edward Almond and OP Smith at the Chosin Reservoir, William Dean, captured in Daejeon, Walton Walker flying over the Pusan Perimeter in a single engine plane, giving orders to his men to hold their positions. So, at what point, even in the modern military, did generals go from soldiers to executives, as it were?