Next you get the second screen, that's [[UIScreen screens]objectAtIndex:1]. Get its bounds by calling the bounds method, create a window, set it to be on the second screen, add a view, and that's it. That's all to get started.
If you want to do it really well, you can ask iOS to tell you when external screens are added or removed, you can ask what resolutions are available and change the resolution if you want. But it's all really easy to do.
Designing a useful user interface may be a little problem, since your external screen won't be a touch screen; so if you put a button on the external display, nobody will be able to press it. Second display is purely for display.