The Andromeda Galaxy is the most distant object you can see with the naked eye. It sits about 2.5 million light-years away, and the faint smudge of light you see left that galaxy when early humans were first learning to make stone tools. On a dark November night, Andromeda rides high in the sky and is one of the best first targets for a new stargazer.

Start by finding the Great Square of Pegasus, four stars forming a large square high in the southern sky after dark in November. From the top-left star of the square, Alpheratz, follow the chain of stars that curves up and to the left: two bright stars, then a fainter pair. That chain is Andromeda, and the galaxy sits just above the second star in the chain, Mirach.

The classic trick is to star-hop from Mirach. Look a little above and to the right of Mirach, and you will find a faint, fuzzy oval. That is the galaxy's bright core. Under a truly dark sky it is visible to the naked eye as a small grey smudge; from a town, binoculars make it obvious. Do not expect a spiral shape with your eyes. The spiral arms are far too faint, and what you see is the concentrated glow of hundreds of billions of stars.

Binoculars transform the view. Even a cheap pair will show the oval core, a brighter centre and a hint of the galaxy's tilt. A small telescope at low power shows the core, the dust lane on one edge on a good night, and the two companion galaxies, M32 and M110, as small fuzzy spots nearby. Keep the magnification low: Andromeda is about six times wider than the full moon, so high power only shows a small piece of it.

November is the best month to try, because Andromeda is high overhead in the early evening and the nights are long. Pick a moonless night if you can, get away from direct lights, and give your eyes twenty minutes to adapt. Use averted vision, looking slightly to one side of the object rather than directly at it, and the faint smudge will brighten. Once you have found it, you have seen across 2.5 million light-years with nothing but your eyes.