I could be wrong, apologies if I am doing you an injustice, but I think you have confused two different but related things.
The button on the side of the camera is to take an actual picture, or in photography jargon 'the shutter release'. However, before you start taking pictures the lens COVER (the dark plastic shield over the lens, which could be described as a shutter) needs to be removed.
The should be a curved switch immediately adjacent to the lens (I think silver in colour and grooved for grip). If you slide this across, the lens cover will open and the camera should start up. Press the button on the side of the phone to take picture.