Look for an identity card with the person’s name on it.
Search on Facebook for the person. The identity card found in Step 1 should help you to pinpoint the exact person (occupation, school, etc), in case of name conflicts.
Facebook message the person and / or any mutual friends.
This is arguably the fastest way of getting in contact with the person in need, without all the red tape involved in police reports or official channels. Assuming he or she has Facebook, of course – or it can be replaced by any other social media channels.
Or you can keep the wallet. Shame on you, scum!
This post was inspired from the recovering of the author’s own wallet just this week.