Cry Havoc, and let slip... THE DOGS OF WAR!

It's true, dogs are over powered, but they can also be under powered..
This guide will take a look into some tactics, a good army composition that dogs work well with, and knowledge of how they work.

How they work

Dogs are a special type of unit that can be released by the handlers, to chase down fleeing enemy infantry, or to charge into the thick of the fight to assist your forces...
Dogs have a strong attack and damage, and can easily tear through lesser enemies such as slingers, light infantry, artillery, and other less armored foes.
They have a special ability (Which is the only way to fight with them) called Release the Beasts.
When you have your dog units, they will stand with the tamers, and wait to be released or told to attack.
Release the beasts (attack) will release the dogs, leaving the tamers behind. The tamers are the actual unit themselves, and will NOT route unless in direct combat. The number of units that the card shows is mostly dogs though.
Something to make sure you know before you let slip the dogs of war, is that.... once the beasts are released, you CANNOT recall them, and disengage them in battle.

Have a large number of slingers on the enemy side, and can't get your infantry to close without getting your forces caught up in a waterfall of rocks? Get some dogs.

Army composition
Any army composition will work, and be used to fight with... except maybe a full legion of dogs, that might not work- and i don't recommend it unless you are facing light units....

The army composition that i have found that best works is a mixture of every type of unit.
Lets start with the General. Your general is the head of your army, so he has to be there... right?
The second type of unit i like to recruit are infantry. Infantry is almost required to fight a battle. I'm not saying you HAVE to have them, but you aren't too smart if you don't have them.
In a battle, you should have 5 units of melee infantry, wether they are spears or swords is completely up to you. In my legendary campaign as Rome, i use 1 unit of Legionaries, 2 units of Veteran Legionaries, and 2 units of Praetorian. I will get more in depth later in this section as to why i choose this set up.
The third type of unit to recruit are your dogs. after all, these are the reason why you are looking at this guide in the first place, right? The dogs are the back bone of the army (in my opinion). You will want 3 units of dogs, or more if you decide to opt out of some of the other unit types i am telling you in this guide.
The fourth type of unit to recruit are your cavalry. MELEE Calvary, not horse archers or tarantines, but actual equites.(if you are rome)
The fifth type of unit to recruit are your Ranged . You will want 5 of these, and for good reason. I'm sure you already know why you want them... Because they are essential to any army and can turn the tides of battles! Just like DOGS!
and lastly, the sixth type of unit to recruit are... ARTILLERY! yes! artillery! you will want 3 units of these as well. they come in handy, trust me... just don't get onagers. those suck.

TL;DR?
1- General
5- Melee Infantry
3- Dogs
3-Cavelry
5-Ranged Infantry
3-Artillery

Now, here is where i tell you why i choose this composition....

General is required. so don't ask about that.
Your melee Infantry... Well, they are key to holding up the enemies infantry, and the reason why we want them is so that the dogs can slip behind and attack from behind (this is not always gaurunteed though, read the section above explaining that the dogs, once released, cannot be controlled.

your legionaries are the basic, call them your... Fingernail... It's essential to protecting your finger, and if you flick someone, you can hurt them with it. But, you can hurt yourself in the process. Legionaries are your first hitters, you want them to be the first ones in the combat, to soak up the damage and to widdle down the other unit they are fighting with so that when your 2 veteran legionaries, who are on the left and right of the fight, can close in and surround the flanks of the enemy and essentially crush them from the outside sides, in. Your praetorians are your back up, but are used to protect your artillery (at least that is what i use them for).

Your dogs are going to be let loose when an enemy is attacking, but make sure that if they are attacking you, that you make sure you are closer to the weaker units, because dogs cannot fight with heavy infantry- they will get massacred. Once dogs are released, they will go for the CLOSEST unit to them to attack, and they will NOT stop attacking THAT unit until the entire unit is DEAD, or they have run off the map, at which point the dogs will turn around and come back into the fight. So it is a good idea to have them in several different spots to attack 3 different light units because this will really tear up the slingers and light infantry, if you are fighting those.
If you are the attacker, it is best to get your infantry into a confrontation with theres, and while they are fighting, let the dogs loose on the ranged units that your enemy has. This will make for a better win for your already tied up forces.

Cavalry are the secondary dogs. use these to kill your enemies stupid little slingers, and chase down the routing forces- you don't want anyone to survive, so when that battle victory pops up, make sure you click continue battle, because in the end, the more you kill the less likely the enemy army is to stay alive on the campaign map.

Artillery... oh lord. just get ballistae, and let them loose. i don't even need to explain this one.

Ranged Infantry.... well, plain and simple, they run after throwing one set of javalins and rout pretty quickly, but if they are left alone, you can really tear into an enemy army while your melee infantry are fighting theres, and your dogs and calvery are making burnt marshmellows out of the enemies ranged.