I have no idea how..

You need to get some kind of toy item with an option like "Play with tiggi3" when you click on it in your inventory. Plushies, beanbags and toys from the Toy Box are a good place to start.

Buy a toy for them at one of the main shops or out of the players shops. Once it's in your inventory, click on it and select the option [Play with --pet--]

EDIT: Arya posted before me.