Instructions
Have your Sims interact with the pets you want to breed. Select the Sim; then click on the pet you want to interact with, and select from the options. There are different activities, such as fetching, feeding and petting.
Select a second pet, so the pets play with your Sim together. Their fondness for your Sim and each other will grow.
Purchase a pet house from the Pet Emporium, and place it in your Sims' house. Click on one of the pets you want to breed, and select "Try for Puppy/Kitten" from the list that pops up. A list of the available mates will appear on the screen.
Select the mate with which you wish to breed your pet. If they like one another enough, they will go to the pet house and the woohoo chime will sound. A random litter of one to four puppies or kittens will appear in a few days. If they don't go to the pet house, try again after your Sims have interacted with both pets more.