Using Paper on a mobile device
Paper is purely a web app and only requires an internet browser. The user interface adapts depending on your screen size, so you'll always have the best experience possible no matter which device you use. Of course, using it on a larger screen will allow you to see more, so you may enjoy that more.
Add to your home screen
There's no separate mobile app or anything, but you can add Paper to your home screen on your mobile device for easy access separate from your internet browser, in the same way you could for any app. For example, on an iPhone, you can visit paper.nu in Safari, press the Share button, then Add to Home Screen.