Start with the Great Square of Pegasus: four stars, each side 13–16° long, enclosing 207 square degrees of almost nothing. That emptiness is the point — the Square is easy to find precisely because it is a hole in the autumn sky. The north-east corner, Alpheratz, is where you leave it.
Andromeda is a chain, not a blob: Alpheratz, then 14.5° north-east to Mirach (magnitude 2.1, distinctly warm-orange), then 12.5° more to Almach. Mirach is the landmark that matters. Everything from here is measured from it.
From Mirach, step 3.9° north-west to μ Andromedae — fourth magnitude, and the only star of any consequence in that direction. Now make the identical hop again. Where the arrow ends there is no star: there is a soft elongated smudge that refuses to come to a point no matter how hard you stare.
That is M31, the Andromeda Galaxy. The ring is its true extent on a long exposure: 3.2° long, more than six Moon-widths, a trillion stars laid edge-on across a span your outstretched thumb cannot cover. No eye collects that. What you actually see is the bright inner core — an oval perhaps a degree across, growing as you dark-adapt. Use averted vision: look a little to one side and let the rod cells off your line of sight do the work.
The same galaxy at Bortle 6, bright suburban sky. M31's light is spread thin over degrees, so sky glow eats it from the outside in — surface brightness, not total brightness, is what loses. By Bortle 6 only the small bright core survives, and finding it takes binoculars and a firm idea of where to point them. Bortle 4, the rural/suburban transition, is where it starts to be worth the drive.
M31 sits at declination +41°. From 41° north it passes through the zenith; from anywhere in Europe or North America it is high for most of an autumn night, which is why autumn is when people finally see it. Watch the altitude readout: this is the window you actually have.
Mirach points two ways. Swing 7.1° south-east instead and you reach M33 in Triangulum — 14.8° from M31, and 2.74 million light-years away against M31's 2.56 million. It is the furthest thing a human eye has reliably resolved without help, and it needs a genuinely dark site: face-on and diffuse, it is fainter per square arcminute than anything else on this list. Either way, the light landing on your retina tonight left home before our species did.