The Andromeda galaxy is the most distant thing you can see with your unaided eye.
On a very clear night, it appears as a smudge of light larger than a full moon.
M31: The Andromeda Galaxy
Image Credit & Copyright: Jacob Bers (Bersonic)
Finding the galaxy is not difficult if you find the constellations of Cassiopeia, Pegasus and Andromeda.
Star map source... http://bdaugherty.tripod.com/gcseAstronomy/constellations.html