How is the magnitude of a star measured? How does one measure the brightness of a star?, I did not find anything on the internet.
A device called a photomultiplier is attached to a telescope. 


The telescope is pointed at the target star and an aperture is
closed down to avoid as much spurious light as possible, and a
reading is taken. The photomultiplier literally count the photons
hitting it.
Next the telescope is pointed at a well-known reference star in the
same part of the sky, the aperture is closed, and a reading is
taken.
Finally, the telescope is pointed at a dark part of the sky, the
aperture is again closed, and a reading taken.


Computer software compares the data from the target star, the reference star, and the dark sky to remove as much noise from light scattered by the atmosphere as possible. It's important to know how much of the measured light is coming from the sky and subtract it from the light measured from the target.

Often, this same procedure is repeated with a series of filters to get the luminosity of the target star at many wavelengths. Searching for a variable star's period requires switching from target star to reference star to dark sky time after time, hour after hour, night after night.

I paid my way through college doing this.