To start the game, set the chairs up in a circle. While this person is gone, choose another player to be the Shabbos Goy. That person stands up and turns a couple of times so that all the other players can see what he or she looks like and is wearing. After the SG sits down again, call back in the person who was sent out of the room. That person then has to go around the circle, asking each player a question.
Questions can be of any sort.
The person goes around the cirlcle once, and at the end must guess who the Shabbos Goy is. If he or she is not correct, the questions begin again. Usually, it only takes one time around. The kids I have played this with have loved it. It gives them a chance to get creative in their answers.