How does Pet Battle experience work?

World of Warcraft now has a feature called Pet Battles, which allows you to fight both NPCs and players with your companion pets. I have noticed while doing pet battles that there are various situations where you get more XP (like attacking higher level enemies with a lower level pet) or don't seem to get experience at all (like if your pet dies during the battle, but one of your other pets still wins the battle for you).

How does Pet Battle experience work? What conditions provide an experience bonus and under what conditions do you get less experience?

Are there any other actions than winning that provide experience for your pets?