Eczema is a skin disease and its most common form is Atopic Dermatitis. Its symptoms are different on different dogs. Normally dogs get red scalp that is itchy. There are few measures, which can cure your dog from this disease. Stop giving it commercial dog food. Try to increase dog's immune system by giving it healthy rich food. Best way to treat it is soak a cloth with Potassium Permanganate and compress it on the affected area. Another way is to add Evening promise oil and Neem Leaf Tea to its regular diet. You can also use Neem Oil on its skin after bathing. This will reduce its itching. Do not use shampoo unless really necessary.
I had a golden retriever that had real bad skin irritations, and the vet said that it was the high protein dog food. And he was right. We changed the food and it went away.