Let me start by saying that not all realms may be subject to this kind of manipulation, as not all realms are have a high concentration of pet collectors. This takes planning and a decent amount of gold to start up.
The first thing you'll want to do is make a post on your realm forums stating that you are selling your own faction's Argent Tournament pets at a non-negotiable price of 1500-2000g (decide based on your realm's current pricing on the forums normally.) MAKE SURE YOU FACTOR IN THE NEUTRAL AUCTION HOUSE CUT.
Next, once someone states the pet the want, start spamming your trade chat saying you'll buy that specific pet for approximately 250g less than the person on the realm forums is willing to pay, once factoring in the AH cut.
Using this, I've been able to make 2000g in under 3 hours on my realm sitting around and doing basically nothing.
Here are the pets based on faction:
ALLIANCE
Ammen Vale Lashling - Item - World of Warcraft
Dun Morogh Cub - Item - World of Warcraft
Elwynn Lamb - Item - World of Warcraft
Mechanopeep - Item - World of Warcraft
Teldrassil Sproutling - Item - World of Warcraft
HORDE
Tirisfal Batling - Item - World of Warcraft
Sen'jin Fetish - Item - World of Warcraft
Mulgore Hatchling - Item - World of Warcraft
Enchanted Broom - Item - World of Warcraft
Durotar Scorpion - Item - World of Warcraft
Tips:
-Always try to maximize profits, but don't go overboard or overprice
-Try to keep other people from noticing what you're doing
-Always sell to the opposite faction, they'll pay a lot more than your own faction will