Does anyone know how I could record some audio on the iphone then change the pitch of the audio?
It looks like you'll want to start with the Core Audio Framework: http://developer.apple.com/IPhone/library/documentation/MusicAudio/Conceptual/CoreAudioOverview/
There doesn't seem to be a whole wealth of information on the AutoTune algorithm, but a good start would be to use a Fast Fourier Transform to analyze the pitch to determine what pitch your audio is actually at. It's a relatively simple to change the pitch from what it is to what it needs to be. For example, A is 440 Hz. Assuming the input is actually 466.164 (A#), and you want it to be A, you adjust the waveform by 0.94387383 (440 / 466.16400). An A# becomes an A.
If you want to achieve an auto tune effect, you'll want to subdivide the recording into tiny audio clips that you can re-pitch individually.
More info on pitch detection: http://en.wikipedia.org/wiki/Pitch%5Fdetection%5Falgorithm