So... I took photos of this whole process, but iPhoto ate them. Grrrrrr.
Anyway, it's not that complicated. This little project started when I saw a lovely linen lampshade for $30 or something like that. I bought the $7 plain white lampshade instead and brought it home. Then I found some coarse linen in my stash that was rougher than I expected it to be when I ordered it online. I rolled the lampshade along the linen and drew my "pattern, leaving about an inch on each side and extra for the seam. The resulting shape of fabric is kind of like a section of a big circle (this is where a photo would have been nice).
Then I used a good old glue stick to attach the fabric to the cheap lampshade. That's right - a plain old glue stick. It was really simple, not messy, and has held up for the month or so since I made this.
Here's the result: