I am trying to get started with iOS Airplay (split screen and mirroring) and it seems like there is pretty much nothing on the web about this. I am looking for a sample app or a step by step tutorial to set up Airplay on my app, basically to share my screen, not necessarily audio or video (although I am fine with starting with that its that is more simple).
Can anyone point me to somewhere helpful to learn more about it (besides the iOS library)?
Have a look at the AirPlay Overview documentation, especially the chapter Enriching Your App for AirPlay.
For mirroring, you don't have to do much at all. If you want different content to appear on the AirPlay-connected screen, you basically have to create a separate UIWindow and set its screen property to the corresponding UIScreen.