As promised, my mother showed me the way. It actually turns out that I was doing things right for the most part, but that my yarn was completely wrong for the needles I was using (oops!) and I was being over-anal and expecting the stitches to look "right" immediately, which they absolutely didn't.
Mum gave me some new needles to match my yarn, and was very patient as I learned. I think what helped the most was the inspiration I felt from her kick-ass knitting bag, circa 1970. Is it not AMAZING?
After much practice and starting over, I'm officially on the knitting path. Here's my first test piece with just the knit stitch:
I then learned to purl, and went on to the stocking stitch:
Now I'm working on my first scarf. I got this great yarn that's fluffy and kind of nobbly (is that a word?) which works really well for me as a beginner because it's forgiving of mistakes and uneven stitches while I get used to holding my yarn and experimenting with tension:
Exciting, right? I'm sure there will be many more knitting posts to come...