Successful up to a point. I have discovered the DEVICE button but do not see SYNC MUSIC (or whatever the term is. I can't leave this window to check) after I have pressed Ipod Shuffle. I see SYNC (only) at the bottom right of the window, but when I pressed this button I could see nothing happening. No lights going on and off, no solid bars filling up from left to right. NOTHING! Nor did I see anything resembling the illustrations depicted in the article for which you kindly provided a link.
HOWEVER: Earlier on (before your second reply) I discovered that if I right-click on one of those little cubes bearing the title of the music I had imported into iTunes, and moved down the menu (again, as I can't leave this window to check I can't say which dish I then clicked -- about 5 or 6 down) I discovered that one click of whichever bar was the most likely did the trick! Why Apple cannot provide this simple solution for transferring music from iTunes to iPod shuffle is beyond me. Or have I lost the plot?!