You now have the power to tame a pet, but you must also gain the skills to train it.
Travel to Thunder Bluff. There you must speak to one of our most revered hunters, Holt Thunderhorn. If he deems you worthy, he will give you the ability to train your new pet.
Holt has bested the most powerful and feared beasts of Azeroth, and commands many strong creatures of his own. His ties to the Earthmother are strong, and you can learn much from him. Good luck, <name>.
A young hunter, I see. Yes, I can bestow you with the skills you need to train and guide your pet. Not only will you be able to teach your pet new abilities, you will now be able to feed your pet, as well as revive it, should it fall in battle.
Now, go forth. May the Earthmother guide you on your path. We shall speak again, at a later date.