As you might already know, the Youtube apps has been removed from the new version of iOS (6). So how to access Youtube on your new iPhone or iPad...etc
You can always use the Safari web browser and access youtube.com as any other website, but the easiest solution is depicted below:
Google has published on the App Store the official YouTube apps to overcome its lack iOS 6.
Better multi-tasking possibilities
Through the application, it is possible to comment or access a selection of videos on a given topic, while watching a movie on your smartphone or tablet. It also allows you to share videos on social networks like Google+, Facebook and Twitter, or by e-mail, on the fly.
The YouTube app is no longer offered (by default) on iOS 6, hence the need for Google to develop its own application.
The installation requirements are: iOS 4.3 or later. Intended primarily for owners of iPhone and iPod touch, the application will be optimized for the new iDevices (iPhone 5).
Downlaod the Youtube Application: here