You can apply ice to the bruise for the swelling. If you fall on your head and injure it severely, the bruise is considered a contusion. Contusions of the legs usually require you to put your leg up, or use a pair of crutches while the leg heals. Abrasions, which are scrapes, are areas of the skin that have had the skin scraped off. Scrapes should be cleaned with hydrogen peroxide and then an antibiotic cream applied with a bandage for at least the first day to aid in healing.
Lacerations are more serious.
This is when the skin is actually cut open. Depending on the severity of the laceration, some may need stitches to keep them closed and heal. Deep lacerations can cause nerve and tissue damage. Any time there is a laceration involved, make sure you have it checked by the child's pediatrician. There are certain areas of the body and certain types of cuts that cannot be sutured.