How do scientist measure light years?

Answer 1

A light year is defined specifically by the International Astronomical Union based on the speed of light in a vacuum.

In terms of what scientists mean when they say "a star is X light years away", they are generally getting that number by calculating the redshift of the body in question. Redshift refers to the lengthening of electromagnetic waves as they travel through the universe. Since the universe is expanding at a known rate, scientists can work backwards and see how much the light from a distant star has shifted toward red in order to determine how long that light wavelength was traveling through expanding space. The more shifted the light is, the farther away the object is.

An exact calculation can yield a relatively precise result for the distance of the object, which can then be converted into the familiar unit of "light years from earth".