Download WoWkémon from WoWInterface.
WoWkémon is installed simply by downloading the zip file from the link above, extracting and copying the contents into your Addons folder, which resides within your Interface folder in your WoW directory.
When you begin your first Pet Battle with it active, WoWKémon will enter its tutorial, with the eminent Professor Birch. He will guide you through the process of using this heavily adapted pet battle system, which has been cleverly squeezed into something as close to the original Pokémon format as possible. You will need to pay attention during the tutorial, as some of the commands are a little counter-intuitive, and intelligently the tutorial doesn't let you progress until you've actually done what it's telling you to do!
Do finish the tutorial on the first battle, though, otherwise it starts from the beginning again on your next battle, and it's not the very fastest process in the world!