To quickly open the Camera when iPhone is locked, press the Home button or the On/Off button to turn the screen on, then drag the camera icon (it's beside "slide to unlock") up.
Yes, you drag up! Clicking the icon will not work. Yea, I was clicking too.
Source: Top of page 92 in iPhone user guide:
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. This post has been scraped in violation of that license if you are reading this post on other than http://www.digital-qa.blogspot.com/.