So you want to start pet battling. You've acquired a few pets from vendors, or friends, or an achievement and you want to know what the fuss is about.
And you may ask yourself: How did I get here?
Oh wait, that's not what you're asking: Where do I begin?
That's what I meant to say: Where do I begin??
Well the first step is to visit one of the Pet trainers in a major city and learn the Pet Battle skill. Then you gotta do enough of the quests they give you to get all three pet battle slots.
After that, instead of pet battling, you should really give your pets a good overview and decide where to start. Because, unless you only have three pets, which is madness, you won't be able to level them all in one go.
If you've looked at the pet tab at all, you've probably noticed that each pet has a different type. There're 10 different pet types: Critter, Beast, Aquatic, Undead, Elemental, Dragonkin, Flying, Magic, Mechanical, and Humanoid. Each of these have different abilities and match up differently. A Beast pet, like this Darkshore Cub has beast abilities that hit extra hard against Critter pets, and weak against Flying pets. It also takes extra damage from Mechanical abilities. And also has an ability that heals itself, which is good.
If you look through all the pets, you start to notice that alot of the same types of pets have similar abilities. So if your goal is to build a good team, you probably want to mix and match different pet types so that they aren't all exactly the same as this would be a) boring and b) easy to beat because if they've got something that matches up well against one pet, they can easily beat your whole team. You also need to start thinking about what you want to do with your pet collection. Do you just want to pick up some of the new pets, or do you want to get a few favorites maxed out? Are you going for World Safari?
Pet Battle Goals
Just like in WoW, there are two types of pet battling: PvP, where you go up against other human trainers, and PvE, where you go up against wild pets or the normal pet trainers. And different pets do better in PvE battling than they do in PvP battling. I can't tell you everything about how to get to your goals, but I can give you a few tips.
Pets in the Wild
If your goal is to just get a bunch of pets leveled to 25, the quickest way is to take them out in the wild. But not every pet will be strong against wild pets. This is because most of those pets are critters or beasts with a few flyers or aquatic thrown in there. The other kinds are much less common but they are often the cooler ones to get. Another thing to realize when you're first starting is that pets need healing. Sometimes after every battle and your heal button has an 8 minute cooldown, so you need to either be near a stable master, or you need a pet that doesn't take much damage, or a pet that can heal itself if you don't want alot of down time.
So when you're starting out you almost certainly want a beast pet, or at least a pet that does beast damage. You could also use either a critter or a flyer to take on those pets that your beast just can't beat up. After that, you can pick a fun pet, like an undead or humanoid or elemental. Just make sure and only use the "fun" pet sparingly if it is going up against something that can hurt it. Taking an undead up against a rabbit, or an elemental against a frog can quickly lead to a hurt or dead member of your pet team.
Pet Tamers are NPCs that you can fight that give your pets tons of experience. They have several pets that are extra strong and they can swap them around when you stun or crowd control them so they are a bit tough. However, because they give you a bunch of dailies that give lots of XP for your pets, and they can also drop battle stones, one of your first goals should be to take them all out so you get the daily unlocked. I'll go into more detail about this later, but the key to crushing them is matchups.
PvP Pet Battles
You can also level pretty quickly, or at least with less flying around, by queuing up against other players. It's more exciting than going against PvE pets because there's someone else there and you don't know what's going to happen. However, it is more matchup dependent than PvE battling. You also don't always know what the skill level of the player you're facing is and, since you don't get Pet XP if you lose, it's more of a gamble to level PvP than just doing PvE battling. Also, you can't capture new pets in PvP battles.
Picking Your Battles
So now you've picked your pets. You've got a Ferocious Beast, a Mean Little Bird and the Cutest Pet Ever and you're wanting to make your way in the world. Just like with WoW leveling, you have to start in the low level areas. For most of you, that's Elwynn Forest or Durotar. So to level your pets, you fly out there, make sure "track pets" is turned on and you start using your Ferocious Beast to murder the native wildlife! And it's awesome! Unless you run up against a green (uncommon) pet or a blue (rare) pet. Then you want to capture it! But that's even more awesome!
So you're killing pets, trying to reach that next level without killing your current team, and up pops a pet with a blue name plate. Common sense goes out the window and you just want to catch it! Unfortunately, your new friend is stubborn and doesn't want to live in its new home. So you gotta convince it to come along by beating it up a bit!
To capture it, you have to damage the pet below 35% without killing the pet. You also can't lose the pet battle or you don't get to keep it. Additionally, if it's a blue or green, it'll hit harder or faster than normal so it may be able to take out some or all of your pets.
So capturing takes a little skill. If your pet matches up too well, like a Beast against a Critter, you may need to swap it after maybe 1-2 hits. Otherwise you might get a critical hit and the pet dies. So you swap and take a different pet and gently tap the pet you want until its health is low enough to capture.
It may take several tries before your trap captures it, which means the pet you were using to gently tap your new friend may be nearly dead. If your new friend didn't bring a gang of other critters, then you're fine, otherwise, you have to use your other pets to convince his old friends to let you keep him—by killing them (it's a cruel world). But after that, you get to keep your new friend! And both of you are happy! Especially if your new friend is another ferocious beast that can help you level faster!
I should mention that there's a pet with an ability that will damage the pet all the way down to 1 health, but never kill it. The Terrible Turnip is your friend in these battles, and it's been going pretty cheap lately. So if you want to catch alot of wild pets, you should probably give it a look!