You enable this feature by pressing the Shift key five times in a row. Or, if that shortcut has been disabled, head to the Control Panel and look for the Ease of Access Center.
Under the Ease of Access Center settings, you should see a link to "Make the keyboard easier to use".
Here, you'll find options to turn Sticky Keys on and off (by ticking or unticking the box), as well as other options that make it easier for the disabled or handicapped to use their keyboards.
There's also an option here to turn off the Shift key shortcut, preventing the accidental enabling of Sticky Keys by pressing Shift five times.