How to find the Andromeda galaxy without using a go-to telescope? In other words, what is the proper technique (star-hopping or other?) in order to find and properly point a telescope to this target? Would a star atlas or other tool/reference help? Can I use the R.A. and Dec. coordinates to find such deep-space objects?
I can recognize the constellations around which M31 is located, but I could never figure out a way to pin-point it. Any help or explanation is much appreciated.
Thank you!
 A: Finding M31, the Andromeda Galaxy is a 2-step star hop from Alpheratz.  The trick is find Alpheratz.
It's one of the four stars that form the great square of Pegasus.  This asterism is easier to find than the bright stars of the constellation Andromeda.  Pick the corner of the square that is most near the constellation Cassiopeia.  It's another easily identifiable constellation nearby.  This corner star is Alpheratz.
The wikipedia graphic doesn't show it, but the other submitted graphic does.  When you look at Alpheratz in the sky, you will easily imagine two curved lines that start from this star and move away the square.  There are matching stars on both curves.  Notice the second pair, notice the distance between the two and line between them.  Imagine that line extends north towards Cassiopeia that same distance.  That's where the Andromeda Galaxy is located.
Fore extra credit: extend that line the other direction, the same distance.  Look with your finder/telescope and you will find M33, the Triangulum Galaxy.
A: If you have a properly aligned telescope with good setting circles, you can easily use the RA and Dec of the galaxy to locate it (or any other deep space object you have the coordinates for).  However, many times you don't have those properly dialed in or you're using an alt-az telescope mount (like a Dobsonian telescope) and need another way to find your target.
Finding M31 by hand with the unaided eye is actually fairly easy.  Here's how I do it and explain it to people.
This is the starfield in question (image lifted from the Andromeda Wikipedia article):

You start at her head ($\alpha$), move down to her neck ($\delta$ and $\pi$) and then down to her waist ($\beta$ and $\mu$).  These stars are all easily visible even in a bright sky.  Now starting at the brighter of those last two stars, $\beta$, you move to the fainter one, $\mu$, and then keep going on that same line a distance equal to the distance between the two stars (The separation is about 4-5 degrees on the sky).  At that point you are sitting right on the core of the Andromeda galaxy.  (You can readily see this on the star chart.)
If you're in a relatively dark sky, you'll be able to see the galaxy with your eyes (although it might take a bit of averted vision to do so).  If you're doing the star hopping with binoculars or the finder scope of a larger telescope you should be able to see it easily enough.  And it's quite easy to do this star hopping through the finder scope, I do it all the time.  And that's all it really takes.  As long as you can see the brighter stars in the constellation, you'll be able to locate the galaxy.
A: This is not a good time of year to observe the Andromeda Galaxy, because it's very low in the sky until around 3 a.m. Around that time, this chart I made some years ago may be helpful:

The starhop indicated there, from Cassiopeia, is OK, but not very exact. I prefer to use the two stars in the middle of Andromeda, Mirach (β) and Mu (μ), which point directly at the galaxy.
A: Maybe I'm the only one who starts at Cassiopeia, but I find it easy to start in the appropriate "wedge" of Cassiopeia (with Schedar at it's point) and follow that towards the bright line of stars in Pegasus (Mirach, etc. ). 
