Pets are not combat units and do not occupy space in your squad or "hand"! A separate slot has been added at the warlords dialog. You will see a list of your pets and, accordingly, you can select one of them as active when you click on this slot.
At the moment, there is one pet, but presented in three forms according to rarity:
You can get these pets by taking part in the The Pet Hunt. To begin the Hunt, you need to achieve League 16 and then complete a special quest chain or purchase a special offer which includes a pet.
There are active and passive Pet skills. Passive skills work regardless of whether the pet is active or not, and moreover, they are summed up from ALL of the pets you have!!! Active skills work only from a pet placed in your warlord slot.