I just learned how to take a screenshot on my Iphone display purely by accident. I was in the process of turning my phone off when white flashed on the screen. When I turned my phone on later I found a screen shot in my camera roll. After tinkering around a bit, I figured out how to do this on purpose:
Press and release the Sleep/Wake and Home buttons at the same time. The white flash of the screen is the Iphone’s way of letting you know the screenshot was taken.
You can even take screenshots of YouTube videos. It’s pretty nifty!