There are two ways to do this, depending on what firmware you're running, and both are very simple.
If you've updated to the new 3.0:
Tap on your "Settings" icon.
Scroll down to "Messages" and tap it.
The first option you will see is "Show Preview"
Slide to the "Off" position
That's it!
If you're running 2.2.1 or below:
Tap on your "Settings" icon.
Tap on "General"
Tap on "Passcode Lock"
Enter your Passcode, if you have one set, and you should!
You'll see an option that says "Show SMS Preview"
Slide it to the "Off" position.