Grow your own food!! It can take a couple tries depending on your own abilities, but growing some of your own foods can help keep costs down. We grow lettuce and tomatoes regularly. And we got very lucky and our new house had blueberry bushes. We also plant various other veggies like zucchinis, potatoes, and green beans. Additionally fresh herbs are very easy to grow. You can purchase any of these in a store however seeds are at a fraction of the cost. Not only will you save money over the standard quality produce from a grocer but you will also get fresh organic food as well upping the overall savings.
There does need to be a commitment though to working witht he plants as well as eating seasonally. It is better for our bodies to get variety and better for our wallets. Out of season fruits and veggies tend to be more expensive because of the cost to transport. They also are typically not organic. Starting a couple tomato plants, lettuce, and some kind of berry (raspberry, blueberry etc) will give you a great start. They are all easy to grow and will harvest quickly.
If you struggle and/or don't want to supplement all your food just having a little bit here and there will help. Image having something as expensive and blueberrys or raspberrys a couple times in the summer. Or being able to have fresh oregano or cilantro? Even if you don't use this as a large money saving tool, it most certainly can be a nice treat.