Airprint isn't an app. It's just some new functions that work with the stock apps and third party apps that implement it.
When you open an app that has a share icon (the square with a little arrow pointing out of it, or sometimes just a curved arrow pointing left) you will see a new menu choice, print. You can select this, and if it detects an AirPrint able printer around you'll have the option to print to it.
So far it is pretty limited, and only works with a few HP printers. This is supposed to change, soon we hope.