When you look at the night sky, you see several stars, some of which are bright and others faint. A star could be faint either because it is inherently less luminous, OR because it is really far away from us. For instance, from Saturn, the Sun will not appear like the brilliant Sun of the Earth, but will look like a very bright star in the sky, which is simply because Saturn is much further away from the Sun than Earth is.
So, to measure the brightness (the scientific term is luminosity) of the star, one needs to know its distance. The main technique to measure the distance to a star is from its parallax (if you want to know as to what it is, please write back). If the star is a variable star (its brightness changes periodically), then one can use the period of the variation to determine the distance to the star.
So, the procedure to measure the brightness is as follows: First, one determines the flux from the star (the rate at which energy reaches us from the star per unit area). This can be done using a CCD camera quite easily. Then, as one knows the distance to the star, one can determine how luminous the star should be to give the required flux.
This page updated on June 27, 2015