Aquaphor and Aveeno Baby Lotion help. Especially straight out of the bathtub, slather on the lotion and then top with Aquaphor. Oh, and remember not to bathe the child too often, as it can exaggerate the dryness.
That is one method on how you can treat the external symptoms of eczema, but eczema itself is actually most often related to diet or some type of allergy that is manifesting itself in this way. I recommend seriously looking at your child's diet and considering cutting out different foods for a period of time and seeing what helps. Common culprits are gluten/wheat and dairy, but even just an excess of processed foods can trigger it.