Classic WoW Level Ten Pet Quest for Orc Hunter
This video covers the Taming the Beast quest chain from the point just prior to Thotar offers you a taming Rod for just a Dire Mottled Boar in Razor Hill. Thotar gives you a series of 3 taming rods, every one is different and will allow you tame beasts in the next order: Dire Mottled Boar, Surf Crawler and eventually an Armored Scorpid.
After getting finished the taming Component of the Quest chain, you have got to head to Orgrimmar and talk to Ormak Grimshot inside the Valley of Honor so that you can unlock your pet managing abilities: Tame Beast; Feed Pet; Revive Pet; and Beast Training.
Eventually, don't forget to visit the Pet Trainer and get the Pet capabilities that you will have to give to see this your companion pet.