Prepare cages, make sure all food, water and litterbox are filled. Have toys for the cats(you do not really have to play with the cats, put a toy in the cage).
Quite the same for dogs, first do any medical care, wash them if needed. Let them eat, drink and put them out in the dog run, they can play together too.
I managed ten pets today. It’s quite stressfull, but doable. Once they get to 5000 adoptability you can take a photo and find an owner.
How do you make money in this game? You get rewarded by finding good homes for the animals!
How to get a cat yard? To play with cats I see I need a cat yard but I don’t see it in the store and my yard is for dogs. Can’t I play with them inside the enclosed building for cats? Cat enclosure is what you are looking for!
Note: Oh, and make sure you are running the latest update of the game because there was a problem were animals kept getting sick.