If Siri doesn’t work for some reason, you could try:
(1) pop out the SIM card and call the provider (e.g. ATT) with the IMSI (number on the SIM) or
(2) Dial (may work in emergency dial?) *#06# and it should display the IMEI (phone identifier). That should also let the provider track down the owner.
Or I suppose you can just bring it to a local store. Boring.