Classic WoW Lvl 10 Pet Quest for Orc Hunter
This video covers the Taming the Beast quest chain from the point just before Thotar gives you a taming Rod for your Dire Mottled Boar in Razor Hill. Thotar will give 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 at last an Armored Scorpid.
Once you've finished the taming Element of The hunt chain, you must head to Orgrimmar and speak to Ormak Grimshot during the Valley of Honor as a way to unlock your companion pet handling abilities: Tame Beast; Feed you could try here 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 your companion pet.