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.
Keep the temperature constant in your house. That means you will have to use your air conditioning system at different points throughout the year. If the temperature fluctuates too much, that can be a trigger for your eczema. During the winter, it may be best to get a cool mist humidifier as well, so that your skin does not dry out.
You should always use sunscreen. This is even more important when you have eczema. Use a sunscreen with an SPF of at least 30 so you don't get a sunburn. Having a sunburn can make your skin even itchier than usual. You could use sunscreens specifically formulated for the face on the entire body. These are generally more gentle to use.