You have received good advice: just go out and shoot with the camera. If you stop thinking about it your eye will find compositions that fit the square format. Sometimes your eye finds a horizontal or vertical rectangle that works better, so just crop at the enlarging stage. That is your right, and responsibility, as a printer.
If the square has you confused, shoot as much as you can. Either it will start making sense, or you'll be looking for a 6x4.5 back.
And when not shooting, look at people who have used it.
A couple of people not named-
Michael Kenna- http://www.michaelkenna.net/imagearchive.php
Lee Freeidlander- http://whitney.org/Exhibitions/LeeFriedlander/Images
Thank you all for this insight and help so far. Please keep it coming. I will look at it all that has been said so far and ponder it over as I am out shooting. I have used some of my composition approaches that I would use for "normal" rectangle shooting with the square format when I took the camera out this past weekend for a trial run. But from what I gather, it is intuitive and should be somewhat easy to transition between the 2 formats.
Great, now I have GAS.
Originally Posted by vpwphoto
But since no one cuts 8x8 film, is it clear that there's any real advantage over shooting 8x10 and cropping at print time? I mean, I yield to no one in my love for square formats, but it seems like if you're going to remove a 2x8 strip from every sheet, you might as well expose it instead and have the slight extra flexibility.
To the OP's question, I think on the whole good composition is where you see it, independent of format. The one thing that strikes me about square formats is that they really won't let you get away with bullet composition (unless you're *trying* for an artificially symmetric, geometric image).
Look at work by Keith Carter, Rolfe Horn, Hiroshi Watanabe, Michael Kenna, Joseph Hoflehner and the numerous photos here and flickr groups like Hasselblad, Bronica SQ, Pentacon Six etc. to see what works and especially what doesn't work.
The rule of thirds still applies with the square.
Another of my pipe-dream ideas, is to print 5x5" negs in my Bessler 45mxt.
The 5x7 format frustrates me as I am limited to contact prints... although I have a 5x7 Elwood, that I just don't have the room to set up. It is HUGE.