I had a hard time with this too till I discovered placing the phone on a table (or other hard surface). I find it easiest to turn the phone sideways (home button on the right). Press both buttons till you hear the click and/or see a white border around the screen. The alternative is to swipe the phone screen with the side of your hand, making sure your hand keeps contact with the screen. You can do it right to left or left to right.
Monica