We know the spectrum of hydrogen very well. It has the same spectral lines everyplace that the conservation laws work. The spectrum from farther stars have the exact same lines, they are just shifted to longer wavelengths while in route to our spectrometers. There is more shift, they farther away the star is. We know how far the star is by known candles. Certain binary stars have identical novas due to one star siphoning mass from its partner. At a certain stage, when the mass is sufficient, these stars nova with the same energy and brightness. By knowing the perceived brightness on earth, we can tell exactly how far away it is.