There are three ways to join custom games
- From the App Start Screen
- From the Friends List
- From the Custom Games option on the Game Types List on the Play Screen
From the App Start Screen
If you've been invited to a custom game you can see your invites on the right side of the App Start screen (the one that has the big dude standing in the middle of it, before you hit "Play").
From the Friends List
If one of your friends is playing in a public custom game, you can join them by tapping their name in the Friend List on the Play Screen.
Note that custom games can be public or private. In the screenshot above, it is a private game so I cannot join unless I've been invited!
From the Game Type List
By selecting "Custom Game" from the list of Game Types on the Play Screen you can then press the yellow "Game Key" button on the top right of the screen and wind up on a screen where you can enter the game code of the game you want to join.