Thank you yet again, Apollos!
It is actually the "UV mapping and texturing" tutorial, by BigTallBill. I'm just floating around, trying to get to grips with enough to be able to understand lattices. I thought that tutorial might further my progress with converting older tutorials to apply to the current version of Blender. It seems I failed miserably with that one.
To update you, in case you were curious ( and I mean inquisitive, not peculiar, hehe), thanks to your advice, a few more failures, and another clean slate, I have eventually achieved a valid cube skin!!! YAY!!!
It seems that, if I had just pressed U AGAIN, after the first time (and getting something akin to the wrapping paper needed to enclose a bicycle, for example), the uv ed. screen would have shown me a nice flat cube!
I still know there's something I'm doing wrong, but thanks to the confidence your advice gave me, I have persevered and got what I was trying for!
It was the edge selecting thing I wasn't sure of. I couldn't find anywhere that told me to select edges for "mark edges" with edge select, vertex select, or face select, and my brain refused to organise the logic there.
Half the battle of understanding how to do things right is to understand how things went wrong.... so that's my task for this afternoon, I think.
Thank you again, Apollos, you are a star!