Identify the repair area. Since there are different types of rugs such as braided, plush, and frayed rugs, its important to see what repair needs to be done first. For a plush or fabric rug, find the cut or rip by pushing in the fabric with a flat edged object such as a butter knife to the back side to identity where the rip is located. Then apply duct tape on the backside of the rip.
Sew the torn edges. For a braided rug whose parts have come undone, remove any damaged strands and re-braid the coils. Use an upholstery needle with linen thread to sew the coils with small tight stitches. For frayed edges of a rug, a heavy thread overlapping the frayed edges, reaching 1/4-inch from the edge with a heavy duty thread matching the rug's color.
Reinforce the rug. For braided rugs, it's a good idea to sew a strip of cotton biding tape onto the edges of the rug with small tight stitches to prevent future unraveling.
Trim the rug. For frayed jute rugs, trim the torn edges with shears. Then with cut a strip of cotton binding tape into a 2-inch thick strip. Fold the strip over the edge evenly and sew it securely with cross stitching. Sew the other side with cross stitching as well.