Hi Alex,
Transparency is rather a confusing term as most often it is a measure of skyglow. You can measure skyglow fairly accurately with a sky quality meter. However, if the air is smokey from burn-off or foggy due to vapour, this also reduces transparency. So, in the end the best way is to simply estimate the naked eye limiting magnitude (NELM). However, this has its limitations as one person's NELM will be different to another's because of variations in eye sensitivity due in part to night pupil size. Confusingly, transparent thin cloud cover can reduce overall transparency but passing heavy cloud can completely block views yet allow good transparency in non-cloud areas.
Naked eye, the old star flicker assessment can give a rough "poor, fair, good or excellent" seeing. In telescopes, estimates of seeing can vary according to magnification. At low magnification, the seeing might appear good but at higher magnification you might judge it as worse.
The Pickering test is more accurate but still ultimately subjective.
See ...
http://www.damianpeach.com/pickering.htm
It is to be noted that the size of the airy disk and diffraction rings will depend on the aperture size. Higher magnification is required to detect the diffraction pattern in larger apertures. At higher magnifications, atmospheric disturbances are more noticeable.
I'll be interested to get other people's viewpoints on it.
Regards, Rob