Old 3G and 3GS iPhones can't install the newest version of iOS and therefore lack many of the new features Apple releases every year, but you don't need a new phone to take a picture of your screen. Since Apple introduced screenshots in iOS 2, the method to capture an image has remained the same: press both the Home and Sleep/Wake buttons at the same time.
Take a Screenshot
To capture an image of the screen, simultaneously hold the Home button on the front of the phone and press the Sleep/Wake button on the top edge of the phone. You'll hear a camera shutter noise and the screen flashes to indicate the screen capture.
Screenshots capture almost exactly what you see on your screen, including the status bar, menus, keyboard, pop-ups and most other system objects, as well as the actual content of the current app. One system object that won't show up in screenshots is the button, if you have it turned on in iOS 5 or 6. Also, if your screen is malfunctioning -- such as lines through the screen or water damage spots -- a screenshot doesn't show the screen as you see it but as it would appear if the screen were functioning properly.
See Your Screenshots
The iPhone saves screenshots to your camera roll, just like photos taken with the camera. Open the Photos app, open the Camera Roll album and tap a screenshot to see it. From there -- just like with photos -- use the Share button to email the picture or, in iOS 3 and above, text the picture.