How to log out of your Xbox Live account on Xbox 360
To log out of your Xbox, simply go to the Help and Settings menu and click the SIGN OUT button.
I can't see the SIGN OUT button
If you can't see the SIGN OUT button, it means there are multiple users signed in to Xbox Live at the time the NOW TV app is running. You'll need to sign out of all the Xbox Live accounts except the one that is also signed in to NOW TV.
Once you sign out of the other Xbox Live accounts, go to Help & Settings on your NOW TV app and you will see the SIGN OUT button.