When I had a lampshade which was beyond redemption, I took a piece of fabric about twice as long as the shade was long. I cut it so that I could put a hem at the top and bottom which would just fit over the rims. I sewed it in a circle, sewed the hems and them threaded elastic in the hems. The gathered elastic fit over both rims and stayed in place easily. I used a printed fabric which coordinated with the color scheme. Mine could be washed in the machine.
By
05/05/2009
You could try holding the iron close to the dented area, and pressing the 'shot of steam' button, to try to soften it up, but then you will have to find a way to wedge something inside to hold it out while it dries. A rolled up towel will probably work.
05/03/2009
You didn't say what the lampshade is made of. If you aren't able to remove the dents, you might consider re-covering the lampshade. If you decide to go that route, here are some instructions: http://www.ehow.com/how_2086753_recover-lampshade.html