Classic WoW Lvl 10 Pet Quest for Troll Hunter
This video covers the Taming the Beast quest chain from the point just just before Thotar provides you with a taming Rod to get a Dire Mottled Boar in Razor Hill. Thotar will give you a number of three taming rods, each differs and lets you tame beasts in the following order: Dire Mottled Boar, Surf Crawler and eventually an Armored Scorpid.
Once you've completed the taming Component of the Quest chain, you must head to Orgrimmar and speak to Ormak Grimshot from the Valley of Honor to be able to unlock your companion pet managing abilities: Tame Beast; Feed Pet; Revive Pet; and Beast Training.
Eventually, don't forget to visit the Pet like this Trainer and get the Pet capabilities that you need to give to your companion pet.