Waste not, want not. That's an old saying and it's just as true today as it was years ago, especially when it comes to food. It may very well save you as much or more money to not waste the food you buy, than it does to coupon and buy on sale and mark downs. No matter how careful you are with saving money when buying food, if you waste it after it's bought, it's money down the drain.
Eat all your lefovers. Never let leftovers get pushed to the back of the refrigerator. Pull them forward and eat them at the next meal. If you can't, or don't want to, eat them at the meal after that. If that doesn't work, freeze, dehydrate or can the food. Most foods freeze well, but low fat dairy and a few others don't, like mayonnaize. While cheese crumbles after being frozen and thawed, it's perfectly good for cooking. Eggs can be scrambled then frozen, gravies and sauces may separate but can be whipped back easily.
Use all of a food. When you buy green onions, do you use all of the tops? How about radishes? If you don't eat them, you're wasting food. Green onion tops can be chopped and frozen or dehydrated and used in soups and sauces. Radish greens are greens, healthy and tasty, although the texture puts some people off. Mince to add to salads or freeze of dehydrate them to add to soup or stew. If you save them over time, you can have dish of cooked greens. It takes a lot, like spinach.
Again, use it all. If you peel apples for any reason, wash the apple first, then save the peels and cores until you have a good batch and make apple jelly with it. Apples have enough pectin to jell without adding anything but a minimum of sugar. Potato peelings can be tossed with oil, salted and baked until crispy for a treat.
Clean out your refrigerator and freezer on a regular basis and make it a point to use up odd bits or things you're not quite sure what to do with. The internet is a huge resource for things like that and a search engine is your friend. Someone, somewhere, knows what to do with a half cup of leftover stuffing, two black olives and a tablespoon of cranberry sauce.