How do LCD displays with passive 3D polarize light?
For 3DTV, there are basically two options for 3D:

Active glasses

This is the most common method today: The TV shows the entire image for the left eye, then the image for the right, then the next for the left and so on.
The glasses have one LCD cell for each eye and make only one of them transparent at a time. This need some electronics inside the glasses and a synchronization between TV and glasses, hence these are active glasses.

This 3D system does not rely on polarization of light, though both, glasses and screen do.

Passive glasses

Passive glasses have a fixed polarization filter for each eye, and the TV has to display the two images with different polarization.

One way to accomplish this is obvious when you know how a LCD works. In the simplest form, the TN-LCD, there are two crossed polarization filters with the liquid crystal in-between:


(Source)
Normally, the liquid crystal twists the polarization plane of the light from the lower filter by 90°, so it can pass the upper filter. If voltage is applied to the liquid crystal, it does not twist the polarization plane, and the light is blocked from the upper filter.

So, the light from the LCD already is polarized, and you could stack a second liquid crystal on top of this to twist the light by 90° for every second image.

But this adds complexity, since you need that additional layer and the electronics to control it.

The second way is to interlace the two images, i.e. the odd pixel rows display the image for the one eye, and the even pixel rows for the other. Obviously, this reduces the vertical resolution to 50%.
Technically, the odd and even pixel rows have to emit light of different 
polarization, but it is for sure impossible to rotate the pixels of every second row: The polarization filter is made by stretching a foil and treating it with some chemicals - how would you make a foil with narrow stripes stretched in different directions?

What you can use instead is a waveplate:



It decomposes light into perpendicular components and delays one component due to a slightly different speed of light in its plane. If the delay is a quarter of a wavelength, an initially linearly polarized wave of light will become circular polarized, which rotates clockwise in the picture above.
If you make the waveplate thicker, so that it delays the light by 3/4 wavelengths, this will also give circular polarized light, which will rotate counter-clockwise.
The trick is: Place a second wave plate (with 1/4 wavelength delay) into the ray, and it converts the light back to linear polarized light. The polarization plane has a certain angle with respect to this second waveplate, and the polarization planes from clockwise and counter-clockwise polarized light differs by 90°. So adding a polarization filter behind allows to select between the clockwise and counter-clockwise polarized light.

And there's another benefit of circular polarized light: If a 3D system uses linear polarized light and the viewer tilts his head a little, the filter for one eye will start to attenuate the "correct" image, and will also start to transmit the "wrong" image. This doesn't happen when using circular polarized light, and for this reason, even cinemas use circular polarized light.