One of the biggest changes my family has made is cutting out processed foods. This means that we try to avoid foods in packaging, when possible. Obviously, this is not possible ALL of the time, but we try to buy foods as close to their natural state as possible. If the food has to be packaged, I look for those with minimal ingredients.
We also try to make more things at home, such as salad dressings, mayonnaise, breads, and pasta sauces. You can really avoid a lot of dangerous additives if you make your own! See the recipe page for tips on how to make more things from your home.