How to return found Apple Watch to the owner?

If you're able to turn on the watch - holding in the long slim button on the side for a few seconds - waiting for the apple logo to appear - assuming there's still some battery left - once on (locked or not) - hold the same button again - and it will give you the option of power off - sos - or medical id. There's a chance that the owner set up a medical ID with an emergency contact (is usually a good friend or family member) you can then call that contact to say you've found the watch - and find out if any of their family or close friends have reported losing one. Its not direct - but it might link you to the original owner.

You can’t find the owner, nobody can find the owner. Hand it in as found property (police if you found it in the street, or a property office there is one for where it was found) and hope the owner guesses where they lost it.