Among the many significant accomplishments of the early Greek astronomer Hipparchus was the creation of the first comprehensive stellar atlas. He plotted the positions of some 850 stars and catagorized those stars into classes of magnitude or brightness.
Many centuries later, the English astronomer Norman Robert Pogson discovered that the brightness scale developed by Hipparchus and refined later by Ptolemy was in fact logarithmic. Each step in magnitude is equal to a brightness difference of 2.512 times. This means that a first magnitude star is (2.512)5 or 100 times brighter than one of sixth magnitude. In 1856, he proposed standardizing stellar magnitude using this relationship, which became known as the Pogson Ratio. This magnitude relation is given by m2 − m1 = − 2.5log10(L2 / L1), where m equals stellar magnitude and L is luminosity.
For more on the topic, browse http://curious.astro.cornell.edu/question.php?number=569
Another way of determining the local visual limiting magnitude is to do star counts in selected areas of the sky.
http://www.phys-astro.sonoma.edu/observatory/observers/limiting_magnitude.html
http://www.imo.net/visual/major/observation/lm
VLM is affected by a number of factors besides the visual acuity of the observer. See http://www.go.ednet.ns.ca/~larry/astro/vislimit.html for a VLM calculator.
A few sharp-eyed observers have seen stars dimmer than seventh magnitude under ideal conditions.
Nowadays many amateur astronomers use an electronic device known as a Sky Quality Meter to quantify sky brightness.
Dave Mitsky