Ancient warfare is at the same time the most covered and least documented in all of history, mostly due to the unreliability of sources. However, all sources agree on several key elements.
For the purposes of this guide, I will be focusing on Asia Minor, Greece, and Rome. The reasons for this should be obvious. If not, feel free to message me.

The Basics:

In early stages, warfare was simple. Troops divided into two categories, ranged and shock. One used missile weapons, the other used force of impact to break the opposing line. To group units closer together is to provide the opponent more opportunity to bombard them, but dispersing troops leaves them vunerable to shock.
Later, though, tactics and differences began to emerge based on location. The isolated Greek city-states adopted the urban militia and phalanx, making the most of tight knit communities. Further East, wide open spaces prompted the development of mobile forces and the importance of archery.
Other cultures, such as Rome or Carthage, adopted bits and pieces of there techniques based on personal need and experience. For the purposes of this game, however, these different cultures, fighting styles, and resources were simplified into the following three categories:

The Hellenic world is represented in the game by Thrace, Macedon, the Greek Cities, the Selucids, and to a lesser extent the Ptolemaic Egyptians.

Phalanx
The phalanx, although originally used in Mesopotamia, is associated mosly with the Greeks and other Hellenes. Basically, it is a heavy block of spearmen overlapping shields. Resistant to shock, the phalanx and the hoplite reigned supreme.
Hoplite Tactics
The tactics associated with the Hoplite or his Phalangite successor are brutaly simple: the charge (Marathon), or the wall (Thermophylae).
In traditional hoplite-to-hoplite conflicts, the phalanx would hit their opponent dead on. One would eventually lose the formation and be forced to retreat, or would stubbornly hold their ground and be literally run over in the othismos, or shoving. In game, this is slightly hard to do because the "attack" move on the hoplite tends to make them loosen up momentarily. But a phalanx that actually manages to walk up to an enemy line is formidable indeed. Use them as a sledgehammer, punching through the enemy line.
In defense, the phalanx is even more devastating. Esentally, the long spears keep opponents away, while the solid block of men means that shock tactics have a hard time breaking the defensive line. However, focused missiles can thin the line enough for heavy cavalry to buldoze a way through. While this works, expect heavy casualties.
Peltast
The value of Peltasts is shown early on, as in 425 BC the Athenian commander Demosthenes hired a company of Thracian Peltasts and used them to annihilate a Spartan Hoplite army. The Peltasts were too light for the heavy infantry to catch and caused disproportionate casualties to their enemy. Then, once the Spartans had retreated to a defensible position, these now javelin-less Peltasts crept up behind their enemy and charged them in the rear.
In short, Peltasts are the Greek all-purpose unit. While they do not excel in hand to hand combat, they are versetile and can be used as light infantry if the need arises. Plus, one unit of Peltasts can generally cause up to 50% casualties to a heavier hoplite unit from range.
Cavalry
Greece had no tradition of cavalry as their hilly, forested land was not suited for hosting large herds. For the purpose of this section, I therefore use the Macedonians as an example. Cavalry was divided into light and heavy, the Greek mountains providing little opportunity for mounted archery. Light cavalry are to chase off Peltasts as well as interfere with the opponents light cavalry in carrying out the same. Heavy cavalry were to be the ultimate in shock tactics, charging into lines. Of course, with phalangites forming the majority of the infantry, the heavy cavalry would have too first break through the screening light infantry and whatever cavalry the enemy used to counter. But if successful, the resultant charge into the enemy's rear would almost invariably carry the day.
Mixed Force Tactics
The ultimate word in Hellenic tactics will always be afforded to Alexander of Macedon, whose victories would define and shape the world for over three hundred years.
At the battle of Gaugamela, he routed a far larger contingent of Persians using a mix of the units discussed above.

His deployment is simply the typical Macedonian deployment. The elite Phalangites would form the center, designed to either pin of smash the enemy center. The peltasts would screen the flanks, throwing missiles to soften up the enemy center and holding off light flanking troops. The cavalry, divided into two groups (Parmenion and Alexander), are positioned just behind their Peltasts.
However, rather than advancing full on, Alexander moved the Phalanx to the right in oblique order while having Parmenion move off left. The Persian right wing immediately charged into the gap.

This created a gap in the Persian line, allowing Alexander to lead his elite cavalry to suddenly hit and rout the opposing General, then swing back and hit the advancing Persian center. In all, it is the typical Hellenic play: Initial skirmish transitioning into Phalanx warfare and heavy emphasis on folding the enemy flank with cavalry.

Aisa Minor and the Middle East gave rise to a very different style of warfare than Greece or Rome, both of them being geopolitical. Firstly, the lack of isolated communities made the polis or the citizen-soldier hoplite highly impractical. Secondly, the flat, arid plains and deserts ment that the heavy lockstep infantry could be easily outmanuevered. The Greeks could hold the cities, but in the open field a different style of combat held sway, practiced by the civilizations represented in-game by Parthia, Armenia, and Pontus.
Light Infantry
It matters not if you call them Eastern Infantry, Light Infantry, or anything else. Their basic usage remains the same. Light infantry are manuverable, able to run faster and longer than their heavy counterparts. This gives them a level of versitility that heavy infantry can't match. Essentially, the idea of light infantry is to outmanuever your opponent and only actually engage once you have an advantage (downhill, in the flank or rear, etc.) in order to rout the opponent before you take too many casualties. However, treat them with the same tenderness you would afford skirmishers. They do not tend to be very confident and using them inproperly (head on charges, exposed flanks, etc.) will not go over well.
Cavalry
Eastern Cavalry are diverse enough to be covered in three categories:
Cavalry Archers
Mounter missile troops. The plains are perfect for their use. Circle around your enemy, hit the flanks, lure away his cavalry and leave him tactically crippled. If he disperses too much, don't hesitate to switch to melee and ride him down -- cavalry is cavalry, a charge will hurt.
Light Cavalry
With the presence of cavalry archers, light cavalry take on a new level of responsibility: Ride down or chase away the enemy skirmishers before they do too much damage. Once they're out of the picture, light cavalry can be used in support of their heavier cousins.
Cataphract
Fully armored, able to ride through a phalanx, heavy enough to smash the stoutest line into pieces. What else is there to say? A cataphract unit is of course subject to the same reccomendations as other cavalry, hitting the flank and so on, but unlike other cavalry they have the sheer weight to get away with the occassional head on confession.
Combined Arms Tactics
I was going to avoid using an example present inside the game, but Carrhae is really to be regarded as a perfect use of manuever on open terrain.
Crassus, a Roman with more money than sense, bought an army and tried to imitate his contemptionaries Pompey and Caesar in using military success to kickstart a political career. His legion was primarily infantry, and was caught in the open desert by a mixed cavalry force. The cavalry archers procceeded to encircle his soldiers and slowly shoot them to bits. When the Romans tried a countercharge by light cavalry (theoretically the correct response) the Parthians countered with a group of Cataphracts that destroyed the last remaining vestige of hope along with the Roman cavalry and Crassus' son.
So what does this tell us, other than that Cataphracts are obviously overpowered? Among other things, the importance of using mobility and thinking ahead in fighting Eastern factions of fighting as Eastern factions. If you get pinned down, you have lost. If you lose the initiative, you have lost. The correct response is to manuever, play for time, and exploit any and all mistakes your opponent makes.

The Celts were a wave of iron-age invaders that swept across Europe, bringing their culture and their technology everywhere from Italy to far England. They either supplanted the locals or were absorbed into their cultural identity. By the rise of Rome, they were very much a fact of life across all of Europe.
The Germanic tribesmen occupied modern day Germany, Norway, and some parts of North-Eastern Europe. They would only come into contact with Rome late in its history, but were indirectly responsible for its rise as well as its fall.

Infantry
The game grossly simplifies the Celts into "barbarians," but preserves their main advantage: Shock. The Celts and Germans have some of the best shock infantry available in the game, being able to rout a line with decent efficiency. The drawback? They are absolutely useless in defense. The morale of these groups is possibly even lover than that of Eastern Infantry, possibly a reference to the lack of training and discipline.
Skirmishers
The benefit given to Celtic skirmishers is the fact that the forested areas they tend to be deployed in are absolutely ideal for ambush techniques, allowing you to station hidden groups around the woods and suddenly striking as the enemy passes by. These rapid strikes can overwhelm the enemy morale as ambushes really do take a toll. Then, as the enemy begins to rout, a shattering charge on whatever remnant of their force still stands tends to carry the day.
Chariots
The Celtic Chariots are somewhat of a paradox, with the highest morale shock value of all units and the absloute lowest defense. They are not the steady chariot archers of Egypt, but rather an ancient relic from the early iron age that had once ruled from Greece and Assyria to the plains and deserts of Persia.
The only real use of war chariots is one massed rush into the enemy line. It tends to smash the enemy order into pieces and rout the weaker units. However, the low defense means that if the enemy does not rout immediately, you will lose the chariots. All of them.
Combined Forces
Compared to the other civilizations, the Celtic factions have possibly the simplest tactics possible. Ambush the enemy, force them to turn and face the small forces, then hit them with a wave of howling, bloodthirsty infantry and a few charioteers thrown in for good measure. Simple, brutal and effective, this tends to chase off any force you may be facing.

Rome is the group so unique, it requires a section of its own. Through assimilation of good ideas and endemic warfare, it evolved past the Hoplite to assimilate the fighting style of the Samnite tribesmen. This newfound knowledge was then tempered through a century of fighting with everyone from the Etruscans of Italy, the Celts of Gaul, or the Greek colonies of Eprius. This gave the Roman legion an ingenuity and a method of war starkly different from the rest of the Ancient World and widely regarded as the culmination of infantry evolution.
Heavy Infantry
Hastati, Principe, Triari, or Legionary; It makes no difference in the long run. Roman heavy infantry have one thing in common: efficiency. Where the Hoplite tries to use weight and light infantry opt for manuverability, Legionaries use the one-two punch of thrown javelins followed up with an immediate charge. They also have arguably the best morale in the game, being the perfect unit to take risks with as you have a smaller chance of failure due to mistakes.
Real world example? The battle of Cannae. Hannibal Barca encircled the Romans on three sides then hit them in the rear with his Numidian Cavalry. but while the Romans lost the overall battle their center hacked and slashed through the enemy encirclement to freedom.
Skirmishers/Auxilia
Roman skirmishers here are to be seen as the same as Hellenic Peltasts, with one crucial difference: Where the Greeks lacked light infantry to repond to flanking attacks, the Roman center is more flexible and can deal with this. Therefore, the Romans do not deploy skirmishers on the flanks but in the center, to weaken the enemy line in preperation for a heavy infantry charge.
Artillery
While many factions have access to artillery, the Romans have a wider variety as well as ample opportunity to use it. As they depend less on manuever, they have more opportunity to set up a fixed position and use artillery to bombard the enemy. This is especially useful when dealing with the Hellenic factions, which advance slowly and give you ample opportunity to pick them off.
Combined Arms Combat
The battle at Pydna was the end of Macedonian dominance in that part of the Mediterranian. The battle started as a skirmish when the two sides tried to collect water from the nearby river.
The Romans used a predominantly infantry setup, although rather than using artillery they supplemented their force with elephants, using them the same basic way as an onager: Smashing a hole in the enemy line. The Macedonian right flank fulded under the elephant charge. However, on the left flank the Phalanx started to slowly push away the legion until the Romans used a feigned retreat to pull the phalangites off their hill and across a patch of broken ground. Their formation broken, the Macedonians were taken apart at close quarters.

I hope this guide was at the very least intresting. To be perfectly honest, I made it as I got tiredof the constant complaints about light infantry and the general uselesness of skirmishers on some of the other guides.
In closing, have fun and see you online.
-Zrut