So how does it work? Think about that 3D cinema experience: differently polarised images play on screen together. Viewers wear special glasses with lenses that allow opposite polarisations through.
In a simple 3D screen, a very fine grating, called a "parallax barrier", is placed in front of the LCD screen. It does the job of the polarising glasses, directing light from each image slightly differently so that at a so-called "sweet spot" about 20 inches in front of the screen the two images are separated just enough that the brain will create a composite 3D image. The downside of this is that since the parallax barrier is a permanent feature of the monitor, then it's always in 3D mode - not much use for day-to-day use, as noted above.
In Sharp's screen, the parallax barrier is created by a second LCD screen - known as the "switching" LCD - which is off in normal 2D mode. When this screen is activated, it polarises in stripes so that it is impenetrable to light from the first LCD screen, generating opaque grid lines in front of the normal screen. The following graphic is from Sharp's background to the process:
The limiting factor on this method is that you have to have your head in exactly the right spot to see the 3D image, so no peering over shoulders allowed. Multiple viewer screens are not much more complicated to make: the parallax barrier is finer and cross hatched instead of striped. However, making the images for such a screen is much harder, since instead of two pictures, the 3D image is created by combining at least four viewpoints.