Team Mystic are led by Blanche, who has this to say:
The wisdom of Pokémon is immeasurably deep. I'm researching why it is that they evolve. My team? With our calm analysis of every situation, we can't lose!
Headed up by Candela, Team Valor are apparently all about Pokémon's strength:
Pokémon are stronger than humans, and they're warmhearted, too! I'm researching ways to enhance Pokémon's natural power in the pursuit of true strength. There's no doubt that the Pokémon our team have trained are the strongest in battle!
Team Instinct - who presumably drew inspiration for their name from one of the teams on The Apprentice - are lead by a chap named Spark. Here's what he has to say:
Pokémon are creatures with excellent intuition. I bet the secret to their intuition is related to how they're hatched. Come and join my team. You never lose when you trust your instinct!