YouTube (for iPad) : Default Playback
Videos, by default, play at the normal half-a-screen size…
YouTube (for iPad) : Full screen Playback
…until you click the enlarge icon which expands the image to full screen.
YouTube (for iPad) : Home Screen
This is what you see when you launch the app.
YouTube (for iPad) : Setting and Channels
Here you can browser channels and tinker with settings.