Petopia is the pet bible. Defer any specific questions there.
Pets can do a considerable percentage of a hunter’s damage even if they are not Beast Mastery hunters. All hunters should focus on keeping their pet alive and on the boss (pet uptime). Check the raiding section for pet talents per each raid: we vary the resistances to give our pets the best chance of surviving.
About meta pet families:
You can tame pets after your level 10 class quest in your race’s starting zone. You cannot do this quest in another race’s zone so complete this before you join any leveling friends. In vanilla, you have 2 stable spots and your current pet, totalling 3 pets to swap from. To tame a new pet, you must dismiss or stable any current pet; you can only swap pets at a Stable Master near most Inns. General practice for taming is switching into Aspect of the Monkey, dropping a Freezing Trap if you are level 20, and then taming the pet. This should give you plenty of time to tame while the mob is CC’d.
The most important part of keeping a pet is making sure it is happy. In the default UI there is a green/yellow/red face that indicates your pet’s happiness. Feeding your pet level appropriate food will increase its happiness; pets will lose happiness over time or if they die. When initially tamed, pets start at loyalty level 1 of 6 called “Disloyal.” At this point, you cannot teach your pet anything. To improve loyalty, keep your pet out while you kill experience yielding monsters. Your pet does not have to participate but it must be summoned; you do not need to gain experience e.g. at 60, but you must be killing non-grey monsters. As a pets loyalty level grows, you will have more training points to spend on pet talents and abilities. If a pet reaches the bottom loyalty rank and becomes unhappy, it will run away from you permanently.
To learn new skills to teach your pets you must first tame a pet with that skill and learn it from them. You can check which pets know which skills at this page of Petopia. Once you tame a pet with a skill you want to learn, stand nearby the pet while they cast it. Each time they use the skill you have a chance to learn it; you’ll get a system dialogue line when you have. Once you have learned the skills you want, you may abandon the pet.
To teach a pet a pet skill you’ve learned, use the Beast Training spell. If you are out of pet training points, you must either raise your pets loyalty or speak to a pet training to reset their points. There are no downsides to untraining a pet besides a small fee. Please refer to the raiding section of this guide for pet talents per raid as they’re largely influenced by which damage resistances are best. The leveling section has notes about pet progression while leveling.