Pet users get a special, smaller action bar they can use to control their pet. Your pet bar disappears when your pet dies. You can modify the auto-cast status of pet spells in the pet spellbook.
While your pet is active you have several buttons to control it:
Attack: Select a target, and hit the attack button. There's a hot key to do it too - look it up in the options/controls menu. Pets will try to get behind their targets when engaging in melee combat.
Follow: This command tells your pet to ignore everything else and just follow you.
Stay: This is useful when you want your pet to stay in place. You can leave it outside of town or a building, go do your business, and then come back to it.
Aggressive: If a monster comes within range of the pet, the pet moves to attack the monster.
Defensive: The pet responds if attacked but otherwise won't act.
Passive: The pet just sits there and does not attack, even if attacked.
If the monster is too focused on you, you can use special abilities such as Feign Death, or have your pet use whatever abilities it has to make the monster angry enough to fight it instead. Learning how to properly manage monster hate can take some time. The goal is to keep both you and your pet alive until the end of combat.
If your pet is in Aggressive mode inside of a dungeon it will typically go crazy and attack every enemy in sight. Change it to Passive or Defensive mode.
When traveling, make sure your pet is not in Aggressive mode. Otherwise, your pet will slow you down by attacking everything you pass. You should either change it to Passive mode or unsummon the pet if you don't think you will need it. At the start of a battle make sure your pet is attacking. If it is standing around, it's not helping. You can use hot keys to make your pet attack faster. To make the pet attack, press Control-1.
Go into a newbie region and use your pet to destroy some monsters. It is funny to have your pet do all the work as you watch! Kill someone with your pet in player vs. player combat! Use emotes (ex. /hug) on your pet! Use powerful pets to scare newbies. They will think it's a monster if they are not familiar with the pets that players can use.
Warlock and Hunter pets will be automatically dismissed when you summon a mount. These pets will return on dismount. This does not affect pet happiness for Hunters. Pets will not attack targets that are under the influence of crowd control (sheep, banish, etc.). Pets, summons and guardians are not susceptible to charm. If you tell your pet to attack a creature, it won't be distracted unless taunted. The pet action bar is greyed out while the pet is confused or fleeing. Pets of other party members display in the party UI. You can see pet health and harmful effects on the pet. You can turn this functionality on and off in the Interface Options menu.
Can I give items to my pet?
Can I name my pet?
Hunters can name their pets. Warlocks cannot.
Do pets take up extra experience?
What classes get pets? Warlocks and Hunters can get permanent pets. Priests can control humanoid monsters as a pet for a limited amount of time. There are other ways to get pets. For example, Engineers can construct pets. There are items that players can find that create a pet for a limited amount of time. Players can also buy non-combative pets that are purely for show.