I'd like to know how to transfer my drawing onto the back of the Wonder Under.
You should transfer your drawing to the paper side of the wonder under. You can do this by either using a light box or taping the drawing to a window and placing your WU on top of it and tracing.
If you have an inkjet printer you could cut a piece of WU slightly smaller than a piece of bond paper, then tape it to the paper and run it through your printer. As long as there is no heat it should work (laser printers use heat so that's a no-no).