The formation I just described is the core of a series of other formations; I listed it first because it is the most flexible, and may be adapted by the addition or subtraction of specialists, the rearrangement of soldiers, or changing the supporting units. The core formation is inappropriate in some circumstances -- here are two examples of relatively simple and versatile modifications:
A = Archers (Byzantine Guard Archers)
M = Melee Infantry (Dismounted Latinkons, Byzantine Infantry, Varangian Guard)
S = Spear Infantry (Byzantine Spearmen, Dismounted Byzantine Lancers)
C = Cavalry (Heavy -- Byzantine Lancers, Kataphractoi)
H = Cavalry (Harassers -- Skythikons, Byzantine Cavalry, Vardariotai)
X = Enemy unit
Anti-Knight Variant: the Sandwich
My basic formation, described above, is best suited to fighting infantry units with relatively low attack power -- they're slow-moving, which causes them to suffer more before melee commences, and they're not likely to slice the Guard Archers to ribbons when they finally reach close quarters. When fighting lots of heavy cavalry, the basic formation would do well to be changed:
AAAAA
CC SSSSS CC
AAAAA
Set the spears to Guard Mode, and disable skirmish mode for the rearmost rank of archers; let the front rank skirmish. Keep the front rank of archers in action as long as possible; archers are more accurate when they don't have to fire over the heads of their own soldiers, which makes each arrow count for more in the early engagement. As the enemy cavalry advance, get the front rank to melt back into the empty rank behind the spearmen, ready to serve as reinforcements after the charge comes; disable skirmish mode as soon as they're in position. The troop deployment should look like this:
CC SSSSS CC
AAAAA
AAAAA
Which presents a strong front to onrushing knights, absorbing their charge and putting your guard archers on more of an even keel if they need to bolster the line at a later stage. The archers are also free to lay down supression fire on those enemies which have not yet joined the press of melee, which lets you play on the advantage of having lots of ranged units. If your archers never get a chance to shoot, you might as well have brought along more lancers. Also, notice what happens in the event that your enemies manage to kill off your lancers:
XXXXX
CC _____ CC
AAAAA
AAAAA
They get a nice salvo of arrows full in the face. Point-blank shots are nasty. Especially cool is if you bring your cavalry around to box them in:
C C
C XXXXX C
AAAAA
AAAAA
You get one of my favorite tactics in the history of ever, Hannibal's Crescent. If they try to rout, send your cavalry back to protect your flanks and prepare the archers to start pouring arrows into their retreating backs. If they flee the field, you've won; if they rally, feed them more arrows. Unless something really weird happened, you've just about won the engagement by this point. (Not necessarily the whole battle, just the bit involving snippy horses.)
Anti-Heavy Infantry Variant: The Bursting Dam
This one's an old favorite for taking down heavy infantry, such as Dismounted Feudal Knights. It's rather like the Sandwich in its intial shape, save that the melee component is comprised of Varangian Guards:
CC AAAAA CC
MMMMM
AAAAA
Normally, proposing that archers should take the brunt of the first charge from heavy infantry would be suicidal. However, Byzantine guard archers have very good armor by archer standards, and they can take a decent beating when they have to. Their purpose here is to trip up the incoming enemy infantry, pinning them in place and possibly taking a few down. By maximizing the amount of time they stay in front, you maximize the accuracy of the arrow volleys they lob at the enemy as they close. Flat trajectories are your friend -- it's a large part of why gunpowder units are so effective. (Apart from the high attack power and armor penetration, that is. Bullets fly pretty straight, which means a fair number of them are going to hit the mark.)
Now, excellent heavy infantry won't be stopped forever by Byzantine guard archers -- Janissaries, for example. The front ranks are going to start looking a little thin, so that something like this happens:
XXXXX
CC AAAAA CC
MMMMM
AAAAA
X_XX_
CC AXAAX CC
MMMMM
AAAAA
Notice that some of the heavy infantry are now contiguous with your Varangian Guards. The Varangians can now fill the archerless breaches, which is all part of the plan; Varangians don't use shields in melee, which makes them more vulnerable in the initial charge. But when they actual crush of hand-to-hand combat begins, their armor-piercing axes are a terror on the battlefield. Bring the cavalry around to encircle the enemy formation, and get the Varangian guards to press forward. Their axes are designed to cut through this kind of foe, and the enemy has already been depleted by arrows, tired by fighting the archers, and demoralized by the sudden cavalry strike. They are, in the immortal words of Thucydides, "pwned".