This is something of a trick question. Do you mean the "basic" polarization that the pixels then interact with?
Perhaps the easy way, if it's not conveniently available somewhere else, would be to obtain a piece of polarizing material with a known orientation, and then find it via experimentation. Many pro filters are made and include a mark, a dot, or something like that to indicate orientation.
in an LCD panel, there are two "levels" of polarization. But in essence, from the back to the front, you have:
reflector
light source
diffuser
polarizer (everything gets polarized to this screen.)
then the "LCD Sandwich" which includes the color filters and the individual LCD cells. I suspect, but don't know, that the color filters themselves are on the viewing-side of the LCD.
I'm not entirely positive of how it works; my 30-seconds on Wikipedia didn't help a great deal, but in a generalized essence:
the LC material also polarizes light. By varying the voltage you apply to the LC cell, you can control it's orientation relative to the "master" polarizer. Turn the voltage off, and it's perpendicular to the master polarizer, and that cell is dark. Raise the voltage slowly, and the orientation slowly rotates until eventually, it's parallel to the master polarizer, and thus, fully "open" or bright.
This is a somewhat simplified and generalized explanation; there's quite a lot more going on depending on the specific technology being used.