Hi. As in app notifications such as new Facebook posts, Tweets and so on?
If you go to Settings > Notifications > Select the app you want notifications for > Turn the switch to green
This should then allow them.
You'd need to be in an area of either mobile coverage or wifi for them to work.
If you still have problems I'd recommend restoring the phone / apps via iTunes.
Vodafone customer since 2004. Attempting to help where I can on the Community
