Many newspapers and magazines have their own apps these days. Those who don’t are probably either part of a larger distribution app or use some sort of other digital service to spread the paper version of the periodical in digital format (e.g. PDF). Pressreader is one of the “larger distribution apps”, allowing you to browse hundreds of newspapers from all over the world- right there on your iPad.
PressReader’s selection is large, but not complete. I checked for Norwegian newspapers (I’m Norwegian) and found very few, then checked for British newspapers which I know a bit about and found more but still far from all- with a lot of big ones missing. Still, the selection is quite good!
When you buy a paper you can download it to your device and read it like an interactive PDF. You can flip through pages like normal or click on headlines to get just the article show in a more readable format. You can jump to sections, browse thumbnails of pages and all that stuff which has become pretty much standard on such apps.
As for pricing, that’s a weird system. You have the above subscription options which are available outside the app and look more complicated than doing one’s taxes. Then you have in-app purchases where you can buy single newspapers at a time for $1. Not a bad price, and it does allow you to be a bit more casual about reading papers rather than have an expensive daily subscription. You also get 7 free downloads to get you started.
As for the app itself, that is free in the App Store.