How do I silence the iPhone ringer / enter vibrate mode?

The iPhone can be silenced with one switch. The upper left hand corner of the iPhone has two volume buttons and a sliding switch. This sliding switch is the ring/silent switch. To place the iPhone in vibrate mode and silence the call ringer flip the ring/silent switch down so that a bright orange circle appears. The iPhone is now in silent mode.

Vibration can be turned off when in silent mode. To turn off vibration, navigate to Settings -> Sounds -> Vibrate -> OFF