To walk a pet, go to the Pets section of the wardrobe. Simply tap on a pet you own and leave the wardrobe. This process is similar to wearing clothing and you can see a preview of yourself with the pet before you leave the wardrobe.
Keep in mind that some places are not pet friendly, so you won’t see your pet when you go inside. For example, you can’t take a pet to Brew Palms, but when you return to Hollywood, your pet will be with you on the street.