School mode on Reading for Fun works slightly differently to Teach Your Monster to Read. You will need to login with a teacher user account or an account with groups.
Open the app and select login.
Select the school tab
Tap "login with your teacher account"
Enter your email and password and tap 'login'.
You will then see a form to enter a player name.
Type a player name to find them.
You can leave your devices on this screen to play with your class. They can type their names in to play the game.
Tap play to play a game with that player.