Put the C3 on Silent Mode.

You can turn off the phone to be safe, but the Nokia C3 can be put into silent mode.
Just go to Menu > Settings > Profile and activate Silent Mode.

April 19, 2012: A quicker and more convenient way is simply to depress the bottom rightmost button, the one with a note icon and a forward slash sympbol for more than a second. This will toggle your general and silent mode profiles! This will only work however if you are into the main desktop opening screen, not in the applications screen menu!