Hi Greg,
I second everything Graeme said, including a mentor. A good mentor is invaluable in teaching how to observe and what to look for in an object. There are things that I wouldn't have picked myself unless my (long suffering! You know who you are!) mentor has shown me or told me. But if you can't get one, this forum is the next best thing I think.
There is so much to learn here with so many resources available at your finger tips. Visit the Observing Forum here and read through as many threads as you can- it'll give you a fair idea of what to expect to see, or what to look for in an object just from reading them. It has helped me no end.
Many of the galaxies are really quite faint- even harder if you live amongst light pollution. And remember, do not observe DSOs (deep sky objects) whilst the moon is out (the sky will be too bright).
When I first started out, I actually held off galaxy viewing for a good year and a bit (except for M104, M31 which are quite bright) when I first started out. I concentrated on polishing up some observing skills by viewing nebulae. And I'm very glad I did as I don't have much of a problem nowadays picking up very faint objects in my scope (what light pollution will allow me to view from my backyard).
My advice would be to start observing some nebulae- the Tarantula (NGC 2070)in the LMC is a good one, as is the Orion nebula (M42). The latter being the easiest to find. Observe these over many different nights and pick out details- dark lanes, folds, shadowing, anything. Some nights on M42 you may even be able to make out lots of dark criss-crossing patterns on the larger wing & eventually you might even be able to pick out the rusty copper colour of the fold on the wings edge as I have. Challenge yourself further and see if you can make out the fainter E & F stars that are tightly nestled against the brighter stars (we call this "splitting" stars) of the Trapezium inside the nebula. Of course different nights will produce different results which are dependent on the seeing & transparency conditions, which is why it's important to keep going back to an object.
Have a look
here for some very helpful info on the Trapezium inside the Orion Nebula (M42).
If you're going for the Silver Coin galaxy (NGC 253), I've come to realise that it doesn't like high magnification, so use low power around 50X. It is quite large and shows up as a long streak albeit on the faint side. Using my 10" dob there was no detail visible but then again I'm viewing thru light pollution.
The Andromeda Galaxy (M31 is another one). It's huge. Again, use your low power eyepiece on this one. You will actually see another 2 little galaxies around it. Two are visible in the same field of view and the other sits just below.
One of my favorite galaxies, Cetus A (M77) is a gorgeous little face on spiral which sits very close (from memory I think only one degree away) to one of the bright stars that makes up the constellation of Cetus. You can go high power on this one. Even thru light pollution, it performs well. On a good night you may be able to make out some of the the faint outer arms as I have.
The above three galaxies are very easy to find!
Go slow- there's plenty of galaxies up there and they won't be disappearing anytime soon.
There was a thread running a while back on galaxy viewing with some good tips that should be of some help to you. You can view it
here.
Also, take a look at this thread
here.
In particular, see post no#6 on the brightest & easiest galaxies to view as posted by Glen Cozens. In that thread, Glen has done five different posts, each giving a great list of different DSO's that are easy to view. Glen is a seasoned observer & his posts are a valuable contribution to this forum.
When hunting down galaxies to view, note the capabilities of your scope's resolving power and light pollution will also play a factor. Once you know what magnitude your scope is capable of then you choose which ones to go after. The smaller the magnitude number, the brighter the object (i.e. mag -9 is going to be brighter than mag -12). Well.. generally speaking anyway, unless you come across a large DSO showing a bright magnitude it may not appear as bright as you thought it should (the Silver Coin galaxy is a good example) because the surface brightness is spread out more.
When you get better at chasing them down, this list
here of the 200 brightest galaxies may come in useful for you. Again, note the mag.!
Have fun and enjoy!!!
Suzy.