Apple cider vinegar clears up a lot of skin problems. You put one tablespoon of the vinegar into enough hot water to make one cup and drink it down. Do this twice a day.
Within just a day or two, you'll notice an easing of your eczema. It should be gone within 2 - 3 weeks. You will need to keep drinking the stuff to keep the eczema away, but you may find you can skip a day or two here and there.
Try Bragg's brand of apple cider vinegar. Other brands may contain other types or strengths of vinegar that don't work as well.
Don't try drinking it without diluting it in water. Vinegar is an acid and can cause damage if not diluted first.
I've noticed that drinking it dries out my skin (that may be just me), so you may need to use a gentle lotion for the dryness.
You may also notice other effects from the vinegar, such as less body odor, better breath (it won't smell like vinegar, and the vinegar's acid kills the bacteria that cause bad breath), improved digestion.