Am I suppose to be turning the piece, back and forth as I knit, etc? In other words, am I suppose to hold the working piece in my left hand, and knit onto my right hand needle? Then turn it and do the 2nd row?
Yes, you're going to stop working in the round and work flat which means you'll wor on the inside of the sock, which is the WS.
You leave the one st unworked on its needle, do not slip it, and you'll go back to it later. This is normal for 'short row heels' on socks.
You might find Silver's sock class
a little easier to follow, though I think if you just do each step as written in your pattern, it will come out okay.