While holding the Home button, press and release the Lock Sleep/Wake button. Your screen will flash letting you know that the screen shot was taken.
I had no idea that it was that easy to take a screen shot on the iPhone. The way this works is just perfect. It is easy to remember since it references the ‘you push the button we do the rest’ habit of taking a picture. It works and gives proper feedback. Sometimes Apple gets it right. Sometimes they manage to get beyond the thinking of engineering and make things really work. Technology companies get often stuck on the technology level. Nice to see when it gets transcended occasionally.