The camera shutter on the Droid X is loud. Candid photos of animals or sleeping babies are more challenging with a loud shutter. Unfortunately, there's no way to permanently turn off the shutter sound. You can however, silence the shutter, as needed. Here's how:
Press the Power/Lock Key until the Phone options box appears, then select Silent mode. This method is good if you are already using your Droid X and want to use your camera silently.
Press the Volume Down Key until the ringer volume is at the lowest setting. This method is also useful when you're already using your phone.
When your Droid X is locked, swipe your finger from right to left, at the lock screen. This is useful when you aren't already using your phone and want to take it out quickly for a photo.