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.

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#1 Skype notifications

Under settings notifications center and Skype do you have show on lock screen enabled. Another thing is they are probably only giving you notifications when you are signed in to the app.