WoW Classic Level 10 Pet Quest for Troll Hunter
This guideline covers the Taming the Beast quest chain from the point just right before Thotar offers you a taming Rod for the Dire Mottled Boar in Razor Hill. Thotar gives you a number of three taming rods, each differs and lets you tame beasts in the subsequent order: Dire Mottled Boar, Surf Crawler and eventually an Armored Scorpid.
Once you have completed the taming part of the Quest chain, you will need to head to Orgrimmar and talk to Ormak Grimshot during the Valley of Honor in order to unlock your companion pet managing skills: Tame Beast; Feed Pet; Revive Pet; see this here and Beast Training.
Ultimately, don't forget to visit the Pet Trainer and get the Pet skills that navigate to these guys you need to give to your pet.