But today I cracked it - so I'm sharing it, in a step-by-step, "for dummkopfen" style - in case there's anyone out there struggling like me:
Step 1: Draw your line. Use any line you like. For this example, I scrawled a curvy one.
Step 2: Write your text.
Step 3: Select the text. Then press the Shift button, and while holding it down, select the line. See how each object has it's own little dotty box around it?
Step 4: I kept doing what I was told and using the Text-->Put on Path, and it never, ever worked. Ever. So don't do anything inside the red circle!
Step 5: Instead, try the Effects-->Generate from Path-->Pattern along Path.
Step 6: Give it a second to do its funky thing, and then the following window should appear. Tweak it to your own taste, and when you're happy, click OK.
Step 7: Give it a second or two (machines need time to think) and it will place a copy of your text on the line you drew (if you ticked the "Duplicate the pattern before deformation" box like I did above - otherwise it will use the original text).
Step 8: Your deformed text can now be played around with in any way you choose. I made a few duplicates and coloured them. The whole exercise took about 90 seconds.