The original rag rug article is no longer on line, but I found instructions on eHow . . . the instructions are for a rag rug 3-foot by 5-foot.
Rip the sheets into long strips measuring 1-1/2 inches wide. Start the rip with a pair of scissors.
Chain stitch with the strips and hook until the chain measures 3 feet long. Chain two.
Single crochet in each chain. Chain two.
Single crochet in each single crochet, ending with a chain two every row until the rug is 5 feet long, introducing new strips of fabric when the previous strip is down to 2 inches. Leave the ends of the fabric loose for a rustic look to the rug.
Cut the last fabric strip, tie it into a knot and weave the end into the previous crochet stitches to complete the rug.
Here is another source for a rag rug made of sheets.