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.
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.