How do I get push notifications from Skype to my iphone 5

Hi list,
I use Skype on my laptop and have recently downloaded it to iphone 5. I cannot get push notifications when someone sends me a message if I am signed out of Skype and I have closed it with app switcher; however, I do get notifications if I am signed in.
From looking at Google posts, it would seem that I should be able to get these notifications, when I'm signed out and Skype is closed. People there are complaining that they can't turn them off.
Google has told me that I have to tap on my profile picture then tap on settings, but all I get when I do tap on my picture is the opportunity to change the picture, nothing about settings.
When I first signed into Skype I had a message about push notifications, I believe I clicked yes to that, but now I can't find out how to get anywhere to check what I might have done wrong.
Hope you can help, sorry if this has been covered before, I have needed to turn email notifications off for a while.
Thanks. Kate.