Avoid processed foods.
Replace 'white' foods (white bread, pasta, sugar) with 'whole' substitutes (whole wheat---not just "wheat", that's still white flour---bread, whole grain pasta. But limit your grain consumption, and choose grains like quinoa, amaranth, buckwheat and millet over wheat.
Increase your consumption of raw fruits and veggies (especially green veggies).
Saturated fats are only found in animal products, processed foods and tropical oils (though the sat fat in tropical oils is different from that in animal products). Reducing your consumption of animal products, and avoiding processed foods will reduce your saturated fat intake. (Especially avoid any "hydrogenated" or "partially hydrogenated" oils,, as they are trans fats, worse than saturated fats. And don't go by labels that say "trans-fat free.' Look at the ingredients list. Products can be labeled "trans-fat free" if they contain less than .5 gm. of trans fat per serving, NOT if they contain NO transfats).
Coconut oil is a saturated fat, but unlike animal sources of sat fat, it is a medium-chain triglyceride rather than a long-chain triglyceride, and is treated differently by the body. It's probably the best fat to use for cooking because it is very stable, and supposedly this type of fat is burned by the body as fuel rather than stored as energy (fat).