Avoid scratching your skin in areas that have eczema. This will only aid in making the skin itchier and will increase the inflammation. It could also cause infection. If you need to calm the itch, try applying a cooling gel or moisturizer. Make sure fingernails are clipped short, as well.
Be careful when you put on sunscreen. You never know what may cause you to have an outbreak of eczema. The higher the SPF, the more likely it is that the sunscreen may cause you to have an issue. Try and find something with an SPF of around 35. That should protect your skin from the sun and keep it in good shape overall.