Seeing and transparency:

There are various ways observers measure their local conditions, some have  a scale of 1 to 10 for transparency and a scale of 1 to 10 for seeing; some have 10 as good and 1 as bad and vice versa. As long as its consistent it doesn’t matter which method you use. I use the following scales, where I is excellent and V is terrible.

Seeing:
Determined using the Antoniadi Seeing Scale, as follows:

I. Perfect seeing, without a quiver.

II. Slight quivering of the image with moments of calm lasting several seconds.

III. Moderate seeing with larger air tremors that blur the image.

IV. Poor seeing, constant troublesome undulations of the image.

V. Very bad seeing, hardly stable enough to allow a rough sketch to be made.

Transparency:
For transparency, I use a scale of I to V, similar to the Antoniadi seeing scale, where I is excellent transparency and V is very poor. Usually if it is V, the haze is so bad the stars are bloated and there are haloes round the brighter ones, so it’d be unusual to be out during those conditions.

I. Very clear and transparent. Milky Way ‘iridescent’. M33/M81 visible

II. Very clear. Milky Way bright but not iridescent. No clouds. M31 visible

III. Clear, some haze visible. Milky Way still visible but not detailed

IV. Milky skies, moderately hazy but observing of brighter NGCs doable/drifting cloud.

V. Poor to terrible. Very hazy, bloated stars, haloes round bright stars, Moon and planets or there’s lot of cloud. Not worth the bother.

Naked Eye Limiting Magnitude (NELM):
I use the NELM method for seeing how dark the sky is (this is determining the sky darkness based on the faintest stars you can see with the unaided eye). However, NELM is rather subjective and does depend on how good, or bad, your eyesight is; one person might be able to see down to magnitude 6.5 while another person, standing right alongside, may only be able to see down to 5.8 or 6.0 – and you need to be properly dark adapted, but it at least gives another experienced observer an idea of what to expect at a given place. On an excellent night here at home, I used the NELM method and got 6.7 in the early hours of the morning when my eyes were totally adapted and the sky was totally clear of any haze and skyglow but, unfortunately, nights like this are quite rare.
A more modern method is to get a little device called a Sky Quality Meter (SQM) made by Unihedron and use that. This is more accurate than using the NELM method but these tiny devices are quite pricey, at over £100. Here, at home using a borrowed SQM, I have had readings of 21, which equates to a NELM of 6.1, this was on an average to good night. An excellent night, such as that mentioned in the paragraph above would have been even higher, around 21.6.