Kinectimals

The game will tell you when the Cat is hungry although you do not need to wait. Just go to your inventory (top right of the screen) and select 'Shop' and then select 'Food' and then buy some food. Come back out of the shop and now select 'Food' from within the inventory and select the food just purchased. This will feed the Cat. 

Now to clean your Cat you need to go back into the Inventory and Select 'Care Items' and then select 'Sponge'. Now you just have to repeat the steps described in "First Contact" but this time soap suds will appear so just cover as much of the Cat as you can. 

This does not have to be done at the same time. You can do one and then the other later or back to back it you want too. Simply open your toy box and select "Care Items" and then choose a sponge to give your cub a bath. Then select "Food Items" from your toy box and pick anything you have available to feed him. You can buy items from the store if you have not progressed far enough along to have unlocked some.