The Rhem map you see above is the result of many hours of sketching, rubbing out, and drawing again until it looked very much as it does now. Then after scanning in, cleaning up, colouring in and texting the result was ready to go online. I thought it was pretty good but I asked Kurt Muller (the Rhem author) to take a look and he has made some corrections and added more details. Hope it helps.
If you have found this walkthrough useful, discovered an error or have a suggestion then let me know: feedback.