Finish the last stitch of the last row on the rug. Leave the crochet hook in place and cut the yarn, twine or cloth strip at a length of 6 to 8 inches.
Wrap the fiber over the crochet hook and pull it all the way through the last loop on the hook. A knot will form when the fiber is pulled through. Remove the hook and pull on the fiber by hand to be sure that it is a tight knot. It will feel like a hard lump.
Insert the end of the fiber tail into a large eye needle. Pull a 2-inch piece through the eye.
Insert the needle just under the final stitch on the rug and pull it through. Continue to slide the needle under the stitches in the final row on the rug, gently pulling the fiber through to hide it. Continue until all except the last inch or so of the "tail" of the yarn is tucked in and hidden inside the final row.
Pull the needle away from the remaining tail end of the fiber. Cut the fiber end down close to the rug with the scissors. Carefully pull on the area of the rug where the needle stitches have been made. The remaining end of the fiber should pull back under a stitch in the rug.
Use the standard finish process to complete the body of the rug.
Cut a pile of 8-inch pieces of yarn or cloth strips for a fringe that will be less than 4 inches long. Form a U-shape with a fiber piece.
Hold the rounded portion of the U shape against a stitch on the outer edge of the rug. Insert the crochet hook that you used on the crocheted rug with the hook portion extended out from the rug edge.
Loop the U-shape over the hook. Pull the U-shape about one-inch of the way through the stitch on the rug edge. Remove the hook.
Lift the tails of the 8-inch piece of fiber through the U-shape and pull tightly. This will knot the fringe to the rug for a finished fringe edging. Continue around the edges of a circular or oval-shaped rug, or add fringe to all four edges --or only opposite ends -- of a rectangular-shaped or square rug.
Chain one after your final stitch of the last row of the rug body. Single crochet in each stitch across the final row. Continue the stitching down the side of the rug, working your single crochet stitches as evenly as possible by using the loops at the ends of the rows. To crochet across the edge of the first row of the rug, use the back loops of the original chain and work a single crochet in each chain; end with the standard finish. Create the edging in a contrasting color if you wish.
Skip one stitch, chain one and single crochet in the next stitch to create a lacy-looking edging. Continue the pattern of single crochet, chain one, skip one stitch around the rug body. End with the standard finish.
Add a few extra crochet stitches in the corner loops of your rug if it is square. This will help the rug lay flat. Skipping these extra stitches will make the edges curl.