Finding your way around
Fall is a great time for galaxy-hunting (we're looking away from the galactic plane, specifically south of it) and the star of the show must be Andromeda, or M31. At least if you're in the Northern Hemisphere. Andromeda is the largest galaxy in the local cluster; the other large galaxy (but smallest of the three large galaxies) in the cluster, M33, is also visible and an easy target in small scopes. It's even a naked eye object under ideal skies. Both are easy to find.
In late fall they will be almost directly overhead in the evening -- they will be setting in the west by midnight. There are 2 easy ways to find M31 and M33:
1. There is a large and prominent asterism with 4 bright stars known as the Great Square of Pegasus. Actually the NE star (Alpheratz) belongs to Andromeda, which looks like a long and narrow 'V' waving in the wind. The second prominent star down the brighter leg of the V is Mirach; its counterpart in the other leg of the V is mu And. Go from Mirach to mu And and extend that line the same distance and you've found M31. You can see this in even less than pristine skies. A little optical aid will get you its satellites, M32 and M110.
If on the other hand you go in the opposite direction from Mirach, the same Mirach-M31 distance, that gets you to M33, the Triangulum galaxy. This one is large but has low surface brightness and is much harder to see.
2. Cassiopeia is the W-shaped asterism that's visible in even poor skies. It's asymmetric, one side being brighter and forming a deeper V than the other. The brighter side points to Mirach, from which M31 and M33 are found as above.
If you have a scope or tracker, you might try for another pair of M31's satellite dwarf galaxies, NGC 147 and 185. These are about 1/2way from mu And to the bright star at the end of Cassiopeia.
The shallower V of Cassiopeia also points to something, a small but bright(ish) planetary known as the Little Dumbbell, or M76. But you'll need a scope for that. Another small planetary, NGC 7662 aka the Blue Snowball, is near the vertex of an equilateral triangle made with the N-most stars of the Great Square (Alpheratz and Scheat). You'll need a scope for that too.
And finally, there's an easy to find galaxy _not_ in the Local Cluster, an elliptical almost in the line of sight of Mirach, NGC 404, the Ghost of Mirach. People report seeing it in binos, but it's tough because of the glare from Mirach.
If you get serious about this, your best friend is a good Star Atlas. The Sky and Telescope Pocket Atlas others have recommended is very handy in the field. A scope with setting circles or GOTO is also handy here. But for visual, bino, and alt-az use, taking wide-field photos, or for showing newcomers around the night sky, the large scale star hopping approach is in fact quite useful.