iPhone recording is simple. You can capture the screen by press the wake/sleep button and the home button at the same time. It will save the screenshot in your photos.

If you want more advanced features. There is a Jailbroken iPhone and iPod touch app names ScreenRecorder which let you  record everything that happens on your iPhone or iTouch. It will be saved at location \private\var\mobile\Media\ScreenRecorder. It is available from Cydia store for $1.99.