If you have setup a GKTurnBasedMatchHelper class which includes a singleton sharedInstance class method you can call Game Center's auto match screen by doing the following:
[[GCTurnBasedMatchHelper sharedInstance]
findMatchWithMinPlayers:2 maxPlayers:2 viewController:self];
The sharedInstance method in your GCTurnBasedMatchHelper should look like this:
+ (GCTurnBasedMatchHelper *) sharedInstance {
static GCTurnBasedMatchHelper *sharedHelper;
static dispatch_once_t onceToken;
dispatch_once(&onceToken, ^{
sharedHelper = [[GCTurnBasedMatchHelper alloc] init];
});
return sharedHelper;
}
You can find a great tutorial on turn based gaming with Game Center in this article on turn based gaming with Game Center.