Then navigate to Notification Center, and scroll down to the app you'd like to change the notifications for. However, notifications can be disabled on a per-app basis in iOS, Android, or Windows Phone settings. For example, Facebook only gives you the option to turn off notifications for '1 Hour' or 'Until 8am' - there's no option to turn them off permanently. Not all apps have the option to disable notifications. Depending on how many messages you receive on Facebook, this could be quite a battery drain for your phone.
For example, Facebook's Messenger app will be able to pop up a notification whenever you receive a message on the service. When you install a smartphone app, there's a good chance it will come with push notifications turned on by default.