bare minimum: raspberry pi, PSU with cable (mini-usb), SD card
download Raspbmc (free) on your PC/mac and install to the SD card (very simple, many guides online)
boot rPi with SD card (takes a few minutes first time).
Download (free) official XBMC Controller app to your iPhone/iPad and pair it with the rPi. Job done!! Airplay enabled on Raspbmc by default so just select it on your iPhone and you’ll see the vid on your telly.
How much do those 3 things cost then?
EDIT About £40.
See, a lot of that is gobbledygook to me. I can see it’s a cheap solution and that’s great for those that can be arsed, and know what they are doing, but I can’t and I don’t.
If I was (And I’m not anyway) going to stream stuff to the TV I’d just go buy an Apple TV because it’s nice and simple and even an eejit like me can get Apple stuff to work in seconds. 🙂