Abrasion wounds should be washed with soap and warm water, and any foreign material like dirt or grit removed. Washing is the most important thing to do, and just about everything else is optional and depends on the severity of the wound.
Loose flaps of skin, if they are clean, can be left alone. They can help to form a natural dressing. If the skin flap is dirty, you can cut it off with very sharp scissors such as nail scissors. Such skin is dead, so you shouldn’t feel anything. If it hurts, it means you are cutting healthy live skin, thus the wrong skin!
Pain from an abrasion can be lessened by the application of an ice pack, but wrap it in a towel. Apply it for a few minutes at a time to help with pain. Most scrapes should stop hurting fairly quickly.
Watch for signs of infection like pus, severe redness or swelling, and fever. Some redness around the wound is a normal part of healing, though.