You will need a cloth lamp shade, RIT dye, salt, and a large bucket that you shade will fit in completely. I used the bottom half of a shop vac for my bucket to get something wide enough (don't tell my dad, I think it was his!).
I followed the instructions for the dye and mixed it on the stove.
The actual dying I recommend doing outside if possible; it can be a little messy.
I just swirled the bucket around a little to mix the dye and dipped in all but the top inch of the lamp shade. Then pull it out slowly keeping the bottom end in the longest. The whole process only took about a minute. Remember you can always dip it again if you want it darker, but once the dye is there it's not going anywhere so it is better to ere on the safe side.
Leave it out to dry for about an hour and it's done.
I added ribbon trim to the top and bottom edge of mine.