By Vatsu in the official forum

Now we get into the meat of combat and the strategy of "Building a Better Army". There's a lot of debate on the subject of who hits who and in what order, and I hope to shed a little light on the subject of the combat order. I don't have the exactly formulas for how combat takes place, but i've seen enough battles to have a general understanding of what "not" to do :P

Frontline and Backline:
The first thing we need to consider is where our troops are standing on the battlefield. Infantry and Cavalry are frontline, Ranged and Artillery are backline. he reason this is important information is it tells you who has to go through who to get to who. Obviously the enemy swords are not going to be hitting your archers if you have swords of your own between them....

Cavalry:
These guys are very tricky to use in combat, you really need to know what you'll be fighting beforehand. Hussars are straight up useless in combat...."Period". Cuirassiers are nice to use at times to punch a hole through a weak division of swords, the 150% damage charge first round can devastate a sword tank. As well you can use Camel Cavalry to counter another person's Cuirassiers. But bear in mind that if your opponent is carrying Pikemen, your cavalry might as well be a water balloon for how long they will last.

Infantry:
Swordsmen will save your life! They have strong hitpoints and are not particularly weak against anything. A strong main Vitality Infantry master will add vast endurance to your fighting force. Pikemen....another one of those finicky units. Pikemen will devastate cavalry in an evil way, but alternatively will get annihilated by horse archers and regular archers. It's not even funny in the least how weak they are against archers.

Ranged:
Archers are your meat and potatoes damage producers. They are consistent, start with 25% crit, and outperform any infantry for damage. Skirmishers are your lifeblood, never underestimate what they can do for you. They protect your ranged units as well as doing massive damage when your enemy has no skirmishers. Muskets are basicly archers that are more expensive and do more damage, not much to say here, just better overall than archers. Horse Archers are kind of a specialty unit like the camel cav and pikes, they will take damage before skirmishers and have more health, but at the same time have to fight the swords before they can hurt the ranged. Entirely up to you how you choose to employ them in your build

Artillery:
These guys are widely debated over on the grounds of their effectiveness and worth. Personally I like to have a hero or 2 full of Ballistas, as these guys provide equal damage to frontline and backline troops. Ballistas don't have impressive overall damage, but the consistent diminishing of backline troops can prove to be a great advantage in a larger battle that lasts many rounds. Catapults are loved and hated fiercely. They don't have a very strong damage to cost ratio, but in late game fights provide a strong suppression of Canon usage as they target Canons almost immediately. Canons are extreme damage for extreme cost. These guys pack an enormous punch for those that can afford them.

Ok, now that we've got some of the advanced combat information out of the way, let's talk about hit order and how to put walls between your enemy and your squishier damage dealers.
Typically it starts with frontline gets hit first, then highest hitpoints. For instance, if you have two infantry heroes with swords on them, the one with the most hitpoints will take all the damage directed at swords "before" the second with lower hitpoints takes any at all.

Hit Orders:
Hussars>....Just don't.....
Cuirassiers>Cuirassiers
>Swords
>Pikes
>Ranged
>Artillery

Camel Cavalry>Hussars
>Cuirassiers
>Camel Cavalry
>Infantry
>Ranged
>Artillery

Swords>Cavalry
>Swords
>Pikes
>Horse Archers
>Skirms
>Archers

Pikes>Cavalry
>Swords
>Pikes
>Horse Archers
>Skirms
>Archers

Skirms>Horse Archers
>Skirms
>Archers
>Swords
>Artillery

Archers>Pikes
>Swords
>Cavalry
>Skirms
>Horse archers
>Archers

Horse Archers>Pikes
>Swords
>Cavalry
>Archers
>Skirms

Ballistas>Swords+High HP Artillery
>Pikes+High HP Artillery
>Cav+High HP Artillery

Catapults>Towers
>High HP Artillery
>Seemingly random splash damage(Please correct me if you know it, I don't use cats much)

Canons>Same as Catapults but without splash

Source: http://forum.caplay.com/showthread.php?t=27212