Step-by-step class guides are on the way!  The 1-12 Mulgore Guide is the first guide to get all the individual class steps.  At the top of the guide, simply select which class you are playing and the page will dynamically update all the steps in the guide for that class (both text and images).  The rest of the guides will be slowly updated overtime to include all the class steps, but you can see how it's going to work with the 1-12 Mulgore.  I want to thank crazyK and his Placeholderguild for helping me out with the individual class content.  They are allowing me to get the 1-60 Alliance guide done while also getting all the class steps done at the same time, so everything can be ready for Classic launch (hopefully).
Combat is turn-based and there is no time limit on each round in a PVE Pet Battle. You can take your time to determine which spell to use next. Some pet abilities have multiple round cooldowns, while others can do extra damage if certain conditions are met. Be creative and have fun testing which combination of attacks works best against different wild pets!

I have tried it a few times. It's good if you're new to the game. Otherwise not so much. I found I leveled slower by using it, as it's suggesting to take the longest possible route usually. Basically following roads everytime, when you could take an easy shortcut. Especially if the shortcut involves a bit of fall damage, it's out of question. The "go here" spots don't also update if you take a shortcut, and then the waypoint arrow points to wrong direction. But perhaps it has been updated since then.
A new quest will pop up once your first pet reaches level 3. It will send you to either Audrey Burnhep in Stormwind or Varzok in Orgrimmar. These trainers will offer a quest chain to battle specific Pet Tamer NPCs on each continent. Defeating each of these NPCs will reward a nice chunk of experience for your pets, as well a Sack of Pet Supplies (which has the chance to drop the Porcupette companion, among the always-useful pet bandages).
Each battle that you win will yield experience for each pet that participated. However, deceased companions will not receive any experience (so make an effort to keep them alive by swaping in a different pet). Experience gains are based on your pet's level compared to the wild pet. Defeating a higher level opponent will grant more experience than a much lower level one, but be ready for a tough fight!