My eczema didn't really flare up until the last year of college, when I was under a lot of stress. Before that, it was so mild I just ignored it, and moisturized. When it really showed up, it was raised, oozing, and just plain nasty. It was so bad, at one point I had a person at a store hand me my bag like I was contagious... I had to start covering it up after that.
What finally got rid of my eczema was first exfoliating the area (usually a bad idea, but what was happening to my arm was that the oozy stuff was preventing the old dead skin from coming off, and there was a layer affect going on). After that, applying moisturizer. Now this step might sound easy, but here are the problems: I can't use synthetic fragrances on that area, and I can't use petroleum products.
The petroleum products thing was actually the hardest. Lot of eczema specific creams use them, and even some of the ones that are suggested by doctors. Eventually, I just gave up on specific ones, and just started using whatever natural moisturizers I could find that contained either no fragrance, or natural oil ones.
The last problem is that I sodium laurel and laureth sulfate really irritate the area, so I can't use soaps that contain those. I can every now and then (like at a restaurant), but prolonged usage causes a flare-up.
I guess what my long story is trying to say is really pay close attention to what you are using. My eczema flare-up of doom was actually prolonged by months before I figured out that it was the petroleum doing it. Once I took away the ingredients that were causing it to remain, it went away pretty quickly, and now I just have to deal with small flare-ups, and the thinner skin in that area.
Also, moisturize after a shower/bath. I know this is repeated over and over, but it is one of the truths of truths to keep your skin moist. It's actually something I tell everyone, regardless if they have eczema or not, because it's so important. A bath is like an antibiotic; antibiotics kill even the good bacteria, baths/showers get rid of even the good moisture/oil. You need to replenish what you took away, and lock in what you have left before it goes out.
Hope that helps at least one eczema sufferer ^_^.