Well, you have to feed them, and talk to them, and keep them clean...oh, and they like to battle each other. When the wild ones pop out at you from the grass, you can send yours out and they'll fight each other, but it's not like cockfighting or anything. You should have some medicine in your bag for them in case they get hurt. Also, you can catch the Pokemon you battle if they're tired enough - for that, you use the red and white Pokeballs.