To determine the orientation of polarization of a new linear polarizer without markings, users can utilize known polarized light sources, such as LCD screens or reflections from shiny surfaces. Observing the darkest view through the polarizer when looking at reflections can indicate the correct orientation, typically perpendicular to the surface. Some users noted that LCD screens often have a consistent polarization angle, aiding in this process. Additionally, checking oblique reflections from clean glass can help identify the polarization direction. The 'true' polarization can be found by averaging results from different angles to locate null points in light intensity.