Studies show that covering up a minor cut or scrape with a bandage encourages new tissue to grow, decreases the likelihood of infection and scarring, and reduces the risk of further injury to the area. Start by cleaning the wound with water, apply an antibiotic cream or ointment to minimize the chance of infection, then cover with a bandage. Change the bandage regularly to avoid infection and developing an allergic reactions to the sticky adhesives used in most brands. Once you notice the wound has healed sufficiently, exposing it to the air will actually speed up the healing process.