Make a list
The idea here is not to buy what you don't need. If your make your list while literally walking around and looking into your pantry, cabinets, freezer, and fridge, you will make a more accurate list. You will also do better if you look at your week's calendar of activities before hand. You may not remember someone's birthday, or that you are attending a potluck for which you need to cook. Then, make your list and stick to it.
Get a freezer
Get the largest most energy efficient one you can afford. It will pay for itself in the long run. Here you will have a place to keep all the things you get on discount, and all the great produce that you grow, forage, buy and put up. If you are lucky enough to get game, fish, poultry or a side of beef from the county fair, you will have a place to store it. Make sure you consult with the health department, fda.gov or other reputable sources about how it is to be properly packaged.
Pick your own
In areas which are near to agriculture, it is worth exploring the " pick your own" options. I have seen farms for cherries, berries, and pumpkins in our area. The prices are better than the store, the produce fresher, and it is more fun.
Unless you are in California, you cannot expect to get everything you want, all of the time. But every place has it's speciality. Take advantage of that. By all means make your local farmer's market a regular stop. It's also great fun and very informative to go to the agricultural part of your annual county fair. Local food supports the local economy, and is fresher since it has not been shipped. Hopefully that savings will be passed on to you.
Shop the sales
Keep an eye on the papers, but don't be obsessive about coupons. Coupons are usually on corporate highly processed brands of low quality and you don't want those anyway.
Stay out of the middle
Most conventional grocery stores put their highly processed and packaged foods in the middle. If you are cooking fresh homemade food you will not need much from there.
Buy in bulk
Balance this recommendation with the recommendation to eat fresh food. If you do have people in your family for whom it is appropriate to eat homemade bread, then by all means buy whole wheat flour in bulk. But remember, you have to use whole wheat flour up fairly promptly. Thus there isn't a lot of point in buying enormous quantities. Non- nutritious white flour will last forever, precisely because it is non nutritious, but you need be buying that anyway. Consider other sources of bulk carbohydrates like Quinoa or frozen corn.
Canned goods such as tomato sauce are worth buying in bulk. But remember, canned vegetables are relatively non nutritious, so avoid them.
Frozen produce keeps it nutrients well. Freezer goods such as frozen meats, poultry, fish, as well as frozen fruits, vegetables, nuts and even shredded cheese are great to buy in bulk. You can always repackage them for convenience.
Buy fresh food in bulk and process it yourself, either by freezing, canning or drying. You must find a reputable source for instructions. There are many fine books on the market. It is very easy to go to any larger grocery store to the section where they have the canning jars and lids. There is almost always a display featuring small books on canning and freezing, made especially by the jar companies. These are reliable if you follow their instructions precisely.
Get a subscription
To a food magazine ? Yes do that. Subscriptions are much cheaper than buying magazines off the rack. And FYI, the best food magazines are on the racks in the checkout rows in the natural food stores. They are full of great information and great recipes, but are usually also full of unfounded claims. Use your judgement when reading. If it seems too good to be true, it probably is. And for a review on critical thinking , check out my section on Information and Learning right here on this site.
Get a subscription to a CSA ! This stands for community supported agriculture. In the growing season You can contract with a local farm for the weekly delivery of seasonal fruits and vegetables and they come ready. This can really work well and be a great value in some area.