M31 is the most distant object we can readily see without a telescope.
HOW TO FIND IT:
Locate the stars Beta and Mu Andromedae. They point almost directly to this galaxy, with its two smaller satellites. With the unaided eye, you should be able to see it as a small cloudy patch of haze
WHAT TO LOOK FOR:
This is the first galaxy many amateurs try to locate, and they often miss it because they are looking for something that looks like its photography. As with all Messier objects, the eye and the camera will see objects differently.
Look for a large, hazy oval.
Once you spot it, look for its satellite galaxies. There are four. Two will be too dim for most small telescopes. These are NGC 147 and NGC 185. The other two are M32 and M110.
M32 will appear as a distinctly separate object from M31. It will be small, round and hazy.
M110 will be a little more difficult to spot, appearing to be dimmer. It will be on the other side of M31 than the other satellite. M32 can be seen with binoculars, M110 will probably need a telescope.
Try to determine how extensive you can see the image of M31. Some have reported seeing this galaxy's glow for almost the equivalent of the 10 full moon diameters.
Look for any dark lanes across the image of the nebula.