When taking a picture with the iPhone, remember that the picture is taken when you take your finger off of the button, not when you touch it. So, get the camera app going, compose your picture, put your finger on the button and keep it there waiting for that perfect moment… and then, very gently, take your finger away. You will get better pictures this way (stabbing at the button to capture the picture at just the right time results in a jarred iPhone, and a blurry picture).
Bonus: remember that that the camera “button” is on the screen– it’s NOT the home button. See below.