if you click on a minion in your zoo you can do some kind of battle with it
Also note that while you can increase your minions' stats by doing battles with them, the feature is not really finished so you don't really get anything out of it right now other than leveling them up, but it doesn't really do anything (and like no prizes and such).
That's why I think there's not really a guide or anything for it right now, because it's just kind of there as an unfinished feature that is probably low on the priority list of things to flesh out since programming resources are limited.