How do users add friends to Game Center? does it simply look at the user's contacts?
How are friends added?
Players can add friends using iOS devices under Settings -> Game Center -> Add friends.
Game Center friends are invited through iMessage conversations with your friends / contacts, yes. These can sent via your Game Center profile, as previously mentioned, via iOS devices under Settings -> Game Center -> Add friends as well as through the new Game Center profile locations in the App Store and Game Center In-game Dashboard.