It’s come up a few times where I’ve needed to get a screen shot from my iPhone. Turns out there are two ways to do it, one of which is built into the phone.
Easiest way is to hold down the home button and press the power button. You’ll hear the shutter sound and the screen shot will be saved into your camera roll. Piece of cake. You’ll still have to get it from your phone to your computer, but that’s not too tough.