Add Friends to Game Center App on iPhone 4S
If you want to play Game Center games on your iPhone 4S with others who have an Apple ID and an iPad, iPod touch, or iPhone, add them as friends so that you can invite them to play.
From the Game Center home screen, tap the Friends button at the bottom of the screen.
On the Friends page, tap Add Friends.
Enter an e-mail address in the To field and edit the invitation, if you like.
Tap the Send button. After your friend accepts your invitation, his or her name is listed on the Friends screen.
With iOS 5, Game Center gained a Friend Recommendations feature. Tap the Friends tab, and then tap the A-Z button in the top-left corner. A Recommendations section appears above the list of your current friends. These are people who play the same or similar games, so if you like, try adding one or two as friends.
You will probably also receive requests from friends who know you’re on Game Center. When you get one of these e-mail invitations, be sure that you know the person sending it before you accept; otherwise, you could be putting a stranger in communication with yourself.