Coupons are your friends. Clip them, collect them and use them. If possible, never buy a food item without coupons if it's not already on sale. Supermarkets often sell items at below-cost prices to attract customers. Buy those. Leave the high-margin stuff alone. Go to a number of stores to maximize the use of your coupons and notice how different stores make money on different items. Buy only the goods that are truly cheap.
Eat foods like porridge grains and plant based foods. Meat, dairy and processed foods take more energy to digest and have the effect of making you hungrier, even though you've consumed more calories!
Grow your food
Try growing whatever comestibles will grow in your environment. Having a spice garden can be a cheap, low-maintenance way to save on spices. Compost and grow a fruit tree or a berry bush in your yard. This will make a big dent in your grocery bills and possibly attract more kids to play in the neighborhood which is a stress reducer.
Learn to cook and eat fresh food and more raw food. Eating healthy is not expensive. The western and developed nations spend the most amount of money on food. Yet they are some of the most obese, malnourished and unhealthy people on the planet. If you're spending more than a couple of hundred dollars a month on groceries, there is something wrong with your eating habits. Volunteer at restaurants, learn about food and how it effects your nutrition. Understanding the role food plays in your life, might be the ultimate key to solving your money troubles and improving your health in the process as well.
Shop at your local grocers that you can reach by walking. Supermarkets usually have slightly lower prices, but the expense of driving forces you to buy large quantities which either interferes with your diet or wastes a lot of money on spoiled food. Smaller grocers have better quality because they can customize. The extra boost you get from carrying your groceries will keep you warm and healthier saving on heating and medical bills.
Junk food is almost always overpriced. Try to cut down. Make your own junk-food such as 'smores or cakes and cookies.