Olive oil. Having toddlers in alaska, we have seen some wicked eczema. We found that a teaspoon or so of olive oil in their bath water works wonders. Moisturizers are useful as well. Just make sure that you check the labels and use natural formulations for their sensitive skin.
Moisture. Lack of moisture is the main problem. Soaking in water, barely drying and then slathering with petrolatum or a petrolatum type product is key. Avoid soaps as much as possible and maybe using soap once or twice a week. There are medications to use such as streroids and immune modulators but it is best to hydrate, hydrate, hydrate, first. Avoid scratching. Mittens or socks on the hands may help.