Skin cancer is becoming more and more common as the kids who were exposed to too much radiation when the ozone layer was thinner grow older and start feeling the effects of the damage. The best way to prevent skin cancer is to be proactive about preventing damage.
Try not to go outside during the hottest parts of the day, and wear sunscreen all year around (even on cloudy days radiation can damage your skin).
Wear sunglasses with the ability to block radiation as well, since skin cancer can even occur on iris of the eye.
This is particularly important for kids, since skin damage when you're young will affect you for years to come.