How do I get notifications on the Facebook app?
 

I don't seem to be getting notifications on my Facebook page ie. when someone comments on my picture, posts on my wall etc. The only notifications I get are about things I have done on Facebook ie. uploading a pic or commenting on something. But when I go onto Facebook on my computer it shows I have lots of notifications. How can I set it up so those notifications show on my Facebook app. Do I have to have it set so I receive a sms from Facebook everytime someone comments, likes my status etc?

Nope, you need the email address that you login to facebook with, being pushed to your device.
So the email notifications can be pushed to your device, and be intercepted by the facebook app to show as notifications.