If you don't have the Facebook app installed
1. Go into your device's default browser
2. Go to facebook.com and sign out of the user there
Go back to Fruit Ninja and attempt to sign into Facebook again, you should now be prompted to provide details to log in.

If you do have the Facebook App installed
1. Open the Facebook app
2. Sign into the account you want to use to sign into Fruit Ninja
3. Open Fruit Ninja and sign into Facebook. The game should now prompt to go back to the app for verification, then return again to Fruit Ninja to sign in.