1. Go to Skype Home (Click your name to access)
2. Go to Profile.
3. Under your avatar should be an option (drop box).
4. Select Public or Contacts only.
Don't have to press accept changes or anything equiv. should automatically do it.
To double check if it has work, check by pressing the 'Public Profile' or 'Contacts Only' tabs next to 'Edit' to see what the public or a contact can see as your profile.
I hope this was helpful!