So I have been playing the MoP beta when time allows and after leveling to 87 I have found myself way more enamored by the new pet battle system and collecting.
Basically you go back to starting zones, fly around and find battle pets to fight, go through the trainer quests, and start beating and collecting wild pets.
Note: You don’t know if any given pet you battle will be of poor, common, uncommon, or rare quality until it is captured (you can tell though by looking at the health and level during the fight so you can always give up early and move on.) Any pet can end up rare, you just have to keep fighting til you find it.
You level up your pets similar to leveling a character from level 1, picking zones where you can find pets of similar level. Don’t go thinking you can go straight to capturing pets while leveling to 87… cause you can’t. The battle pets found while leveling in MoP are a much higher level than yours starting out. Hopefully Pet Battles will be added pre-expansion so we can get some pets leveled up prior to venturing out into Pandaria.