Smurfs Village is all about syncing up with your friends and building a beautiful village to share with them as well. You can add new friends in two different ways. You can add Smurf Village players as Facebook friends and add friends in Game Center. Regardless of your preference, one of the first things you should do is sync your game with Game Center through your Apple device.
If you state Add Me you are implying you want to be added through Facebook. If you want to be added through Game Center leave your ID.