Contact the Animal Control agency in the city/county in which you found the animal to notify them of the found animal. Animal Control will complete a "Found Report" with your information and the information of the found animal. Some Animal Control agency’s will require you to bring the found animal to their facility to complete a report, which isn’t a bad idea since you can get them scanned for a chip at the same time.
If you chose to complete your Found Report via telephone, take the animal to a local veterinary hospital to see if he/she is chipped.
Post flyers in and around the location where found. You may also want to post Facebook and/or Craigslist as well. Keeping the animals safety in mind, you will want to leave out a detail about the animal that the owner would be able to identify if claiming the pet, such as male/female or a certain trick the dog can do to ensure they are the rightful owners.
If you cannot find the owner, take animal to the Animal Control agency where you completed the report
Many people forget that people do look for their animals and if not turned into the shelter or at least notify the shelter, they can't reclaim them.
Remember that safety is always firsts, not just for the pet, but for you too. Always approach a pet that you don’t know with caution. Let them smell you, pet under their chin and don’t pick them up right away if they are little. Make sure the pet is comfortable with you handing it to avoid getting bit.