Well, the first step is to remove triggers. All of the child's clothing and bedding should be washed with detergents designed for sensitive skin. Soaps and other toiletries must also be selected with care. Make sure bath water is not too hot, that will dry out skin. If the air is dry, you should apply a moisturizer or Vaseline immediately after the bath. Perfumes and hairsprays should be avoided.
Is it possible that something in the diet is aggravating the eczema? How old is the child, and how long has the eczema been going on?
But in terms of actual medicines, a hydrocortisone creme is the most effective option. Use it sparingly, however, to avoid thinning the skin.