Here's how to change when the app notifies you of a turn.
Go to the home screen of your device and tap the Settings button.
Find Words With Friends in the list of apps and select it.
From here, you can adjust things like sounds, badges and notification center participation.
Open Words With Friends.
Tap "Menu" button. Then, tap 'Settings'.
In the Miscellaneous section, you can turn on and off background notifications.