In most older speakers, the cloth covering the front of the speaker is stapled directly into the wood of the speaker cabinet. However, more modern designs have the grille cloth fastened to plastic frames. This makes it easier to remove the speaker covering. If the cloth on the grille is damaged or stained, you can replace it using some simple tools and replacement cloth.
Pull the grille cover off the speaker. Plastic grille covers snap onto the speaker, so you can pull it off with your hands.
Put the grille face down, and slide a sharp utility knife underneath the edge of the fabric to loosen the glue holding the cloth onto the frame. Try not to cut the cloth, because you will use it as a template for the new cloth.
Lay the old grille cover on top of the new fabric, and mark the outline of the cover with a piece of chalk. Cut out the new grille cover with a pair of scissors.
Lay out the new cloth, and place the grille, back side up, onto the cloth, centring it in the middle of the fabric.
Apply a drop of glue from a hot glue gun on the upper right corner of the back of the grille frame. Fold the cloth onto the glue, and hold it until it sets. Repeat with the lower left corner of the frame and fabric, stretching the fabric so it is taut before you glue it down.
Glue the lower right corner of the frame, stretching the fabric taut and then gluing it down. Repeat with the frame's final corner in the upper left. Apply a thin bead of glue onto the right side of the frame, and glue the fabric down along the side. Follow with the left side, then the top and bottom to complete the project.
Be sure to use speaker grille cloth. It is acoustically transparent and designed for the purpose. You can purchase it at a variety of sources online.