I often read in books that it is hundreds of millions of light years away from the earth, and I am curious about how scientists measure it. ...

There are probably two algorithms, but I didn't check the specific information. According to my understanding, let me give you an idea:

First, according to the brightness measurement. The brightness of the same light source is inversely proportional to the square of the distance. The stars that we can see with the naked eye are basically stars. Stars have their own laws of evolution. Stars of different ages and masses have different spectra and brightness. People can calculate the brightness of stars according to their mass and age. For example, a star with the same age and mass as the sun, we can calculate the distance by observing its brightness.

The second is based on the expansion of the universe and the red shift of the spectrum. The farther away the star is from us, the greater the red shift of the spectrum. According to the offset of the spectrum, the distance can be calculated.

I don't know how much you know about this, but you may not know it very well. Communicate more.