This is done as an ordered sequence during a wet-to-dry dressing change, and the order is the useful part: the packing comes out, then the wound is cleaned, then new packing goes in.
Taking the old packing out. Wash your hands thoroughly with soap and warm water. Put on a pair of non-sterile gloves. Carefully remove the tape, then the old dressing. If it is sticking to your skin, wet it with warm water to loosen it. Remove the gauze pads or packing tape from inside the wound. Put the old dressing, packing material and gloves in a plastic bag and set it aside.
Cleaning the wound. Put on a new pair of non-sterile gloves. Use a clean, soft washcloth to gently clean your wound with warm water and soap. Rinse your wound with water. Gently pat it dry with a clean towel. Do not rub it dry. In some cases you can even rinse the wound while showering.
Looking, while you have it open. This is the part that gets skipped. Check the wound for increased redness, swelling, or a bad odor. Pay attention to the color and amount of drainage, and look for drainage that has become darker, thicker or foul smelling. Then remove your gloves into the bag and wash your hands again.
Repacking. New gloves again. Pour saline into a clean bowl and place the gauze pads and any packing tape in it. Squeeze the saline from them until they are no longer dripping. Place them in the wound, carefully filling the wound and any spaces under the skin. Avoid putting the moist gauze onto the skin. It goes only into the wound. Cover with a large dry dressing pad held with tape or rolled gauze.
Afterward. Put all used supplies in the plastic bag, close it securely, put it inside a second bag, close that, and put it in the trash. Wash your hands again.
Two things that are easy to miss. Your wound should not bleed much while you are cleaning it, and a small amount of blood is OK. And as the wound heals, you should not need as much gauze or packing gauze.