Lay the felt out flat on the floor and place the rug over the top of it. Cut around the perimeter of the rug, giving an extra half inch over the size of the rug. If it is a round rug, cut small "V"s into the edge of the felt at 4-inch intervals.
Turn the rug over so that its face is on the floor and the felt is facing you. Fold a double seam along the raw edges of the felt, so that the felt is now around ¾ inch smaller than the size of the rug, and pin the seam down. For round rugs, fold over each tab between the small V-shaped cuts to create the seam. Take the felt off the rug and sew the seam together on the sewing machine.
Replace the felt on the rug. On a medium heat, iron the felt flat on the back of the rug. If your rug is made from very delicate material, or is in any way affected by heat, do not iron, but press the felt as flat as you can with your hands.
Thread the needle and thread. Tack the felt to the back of the rug, starting from the center. Sew a line down the center of the rub back, then move around 4 inches to one side, and sew another line, before sewing 4 inches on the other side of the center. Keep going in this way until the whole felt backing has been tacked on.
Sew the whole perimeter of the felt backing onto the rug back.