To get to the games list, from the Main Menu, tap "Multiplayer" and select "Turn-Based". The list will include all games you are currently playing. You can easily switch between games by going back to the list. The games are organized in 3 sections:
To create a new game, tap the + button in the dialog's upper-right corner.
The first step in creating a new game is to select the game time. Once selected, the Game Center UI will be displayed. By default, the game will be matched with a random opponent. To play with a friend instead, tap the Invite button then select one of your Game Center friends. Tap Play Now to start the game.
Once you start a game, it will always be your turn to play. If you are being matched to an existing game, you will first see your opponent's moves being applied. You can then make your moves. At the end of each turn, your moves will be submitted to Game Center. Your opponent will receive a notification letting them know it is their turn.
When a game is completed, it will move to your Completed Games section within the games list. You will then have an option to delete the game when selected. Once the maximum is reached, you will need to delete one or more games in order to create a new game.