How to download apps on iphone5?

I just got an iPhone and I know I can go into the app store and download things, but there's one in particular I want (People Magazine Mobile). I search in the app store and even iTunes and nothing comes up. People.com says to download it from iTunes.com. Do I have to do that, and if I do, how do I transfer it to my phone?

Added (1). Also, I have never had a smart phone before.

Go to the apps stow and search the one you want

Same way as with the iphone 4 you open the app store app, type in a keyword, pick an app, then hit buy or download (depends if its free or not).
but for your problem i will recommend downloading the ibooks app and looking for it there (or look in the newstand)

if you download it through itunes on the computer just plug your iphone up to the computer open itunes and go to sync

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