How to Add Friends to iPad’s Game Center
If you want to play Game Center games on your iPad with others who have an Apple ID and an iPhone, iPod touch, Mac with Mountain Lion or later, or iPad, follow these steps to add them as friends so 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 the Add Friends button in the top (shaped like a plus sign).
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 name is listed on the Friends screen.
With iOS 5, Game Center gained a friend Recommendation 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 can tap the Points tab to view the points these folks have accumulated so you can stay in your league.
You will probably also receive requests from friends who know you’re on Game Center. When you get these e-mail invitations, be sure that you know the person sending it before you accept it — especially if you’ve allowed e-mail access in your account settings. If you don’t double-check, you could be allowing a stranger into your gaming world.