If the pet has no form of ID, have the pet scanned for a microchip (free service at most veterinary clinics).
*Note that some of the newer chips are on a different frequency and will not be picked up by older chip readers.
Go back to the area in which you found the animal after work hours. Ask people you see in the area if they know anyone who has a pet like the one you found.
Take a picture of the pet and post found pet flyers in the neighborhood where the pet was found, at local veterinary clinics, pet groomers, pet stores, and local businesses.
*Always ask permission to post a flyer from the business owner.