Download and install software from the resources section for viewing existing telescopic observations. Ground based telescopes cannot detect extremely distant galaxies and the Hubble Space Telescope can only detect Cepheids (the stars from which other unknown distances are gauged) roughly 6 times more distant than ground telescopes.
Locate a Cepheid variable star within the galaxy whose distance you wish to find. A Cepheid variable in this case will represent the marker for which we will compare to bodies of known distance and luminosity, known as standard candles.
Determine the period of variability of the Cepheid. Measure this against the periods of stars with known luminosities in our galaxy, in order to determine its brightness.
By measuring the brightness (magnitude) of the Cepheid in the distant galaxy, you can determine its distance using the inverse square law. Where R = 10 ^ 1+0.2(m -- M) parsecs, input the absolute magnitude m and apparent magnitude M to solve for the distance of the galaxy.