I bought a full size tan sheet (poly/cotton blend) and a large bottle of dark brown Rit dye.  

I folded my sheet in half and half again.

I held the sheet by the corner (so the sheet looked like a ghost).  

I then tied off every 4 inches with a shoe string (I opted not to use rubberbands, because I didn't want too much distinction between the two colors).

I filled a small cooler 3/4 full of cold water and 1 cup of sal, then added the dye.  I put in the sheet and soaked for 20-30 minutes.

I dumped the water (in the yard!) and rinsed the sheet with a water hose for about 10 minutes.  

Without untie-ing the sheet, I left it to dry outside for about an hour.  

I then wrapped the sheet in an old towel and dried in the dryer for two cycles.

Here are the results:
Brown Backdrop