I assume that you've already opened an application that you'd like to make a screenshot of.
Now, simply press and hold the Home button (shall I mention that this a button at center bottom of the iPhone?), then press and release the Sleep/Wake button (the one on top right of the iPhone).
Your iPhone will flash briefly and the screenshot will be added to your camera roll.
You can now open the Photo application and view the screenshot there.
If you liked this tip, you may like to check out a post listing all of my beginner tips.