I don't know for sure, as I have not kept up with these things lately, but these are probably using liquid crystals. These "shutter glasses" have been around for some time with stereo imaging. That allows the polarisation to be switched and stay in synch with the two serially transmitted images, taking the left and right image to each eye. Whether it is circular polarisation or not probably doesn't matter, it just needs cross polarisation (say clockwise and anticlockwise, or vertical and horizontal), and probably the liquid crystal filter that is used happens to be circular.
As explained by another answer for radio wavelengths, I expect the process is similar and due to the alignment of the liquid crystals themselves. The advantage of the liquid crystal is the polarisation can be switched electrically to produce a shutter (on/off action). There was a camera that used this approach for the shutter too (Cannon).
For an experiment, take polarised sun glasses and rotate them while you are looking through them. The light from the sky is polarised in one plane. As the glasses are turned around to the opposite plane (say vertical from horizontal) the sky becomes darker. When it is say 45 degrees between these two points, it is intermediate. The eye compensates for brightness change with the iris, so the effect is hidden to some extent, so do it quickly.
Circular polarisation can pass a linear polarised filter too with some loss. However it needs to be cross polarised to get enough switch off to act as a shutter.
Search for and follow up liquid crystal displays and 3D. I doubt you can make it yourself, any more than making a car part or an electronic component. The 3D marketing we now have? This must be the 10th time in my life 3D has surfaced, like hula hoops and yoyos, but it may just relate to liquid crystals being finally fast enough switching from on to off to do a good job of this. Also with LCD TV displays, it is probably possible to manufacture the display so the required switching of polarisation is provided at the source as a flat screen. Or it may be a panel in front of an existing display. The LCD flat panel uses similar methods of polarisation to turn individual colours and pixels on and off, or set them to intermediate values.