The short answer is spectroscopy. We can recognize the chemical signature of elements in the stars. When those spectral lines are shifted toward the red end of the visual spectrum, we know it is a "red shift" caused by the object receding from us.
Hugh Bartlett
Hugh Bartlett
"Praise the Lord for the expanding grandeur of creation, worlds known and unknown, galaxies beyond galaxies, filling us with awe and challenging our imaginations." 2007 Reform Siddur