Summarize:

Start by washing the skin tear and the surrounding skin with warm water. Use your hand to gently wash the area. Do not rub or scrub the area, as this can cause more damage to the skin.  Avoid using a towel or cloth to wash the area, as this can irritate the skin tear further. Your hand and running water should work just fine. Make sure you clean the skin tear before you apply a new dressing or bandage to it. This will ensure no bacteria is present in the skin tear before you bandage it. You can also apply a saline wound cleanser to the skin tear. The wound cleanser will contain water and antibacterial ingredients to help clean the area. When you apply the wound cleanser, do not rub or scrub the area. This way take 10 to 20 minutes. You can also use a soft towel to pat the area dry, being careful not to rub or scrub the area.
Wash the skin tear with warm water. Use a saline wound cleanser. Allow the skin tear to air dry.