One of the best ways for me to help my family save money (besides cooking/baking) is to cut our grocery costs. The catch, however, is that we eat whole, natural foods and are a high produce eating family. I serve at least one fresh vegetable (big servings) at every main meal and sometimes a salad and/or a fruit in addition to that. My boys snack on fresh fruit daily. We have salads as part of our evening meal each night. If we are eating beans and rice we usually have an avocado in addition to greens or another green vegetable. Of course, I also use produce in my cooking: onions, garlic, etc.
In my area we have many farmers markets, but surprisingly they aren't the places with the lowest prices on produce, and I have never met a vendor who would negotiate on prices much less sell produce at a discount at the end of the day. They just pack it up and go to the next market, which is probably fewer than 12 hours from closing time as there are morning and evenings markets everyday of the week throughout the greater geographic area. I suspect that farmers markets here have a niche, trendy thing going for them rather than being the place that growers truly discount and sell produce.
On average I go to four stores each time I shop for food, choosing from Costco, Trader Joe's, the health food store, one or two supermarkets, and sometimes the produce stand, depending on what we need and what is on sale. I also order from Amazon using their Subscribe and Save feature plus Amazon Mom to save 20% on my monthly orders, and I belong to Azure Standard, a food co-op. This is a lot of stores/suppliers to manage!
I start by looking at the sales flyers and finding out what the produce sales and loss leaders are. For example, we love cantaloupe in summer, but I will only buy it when a large cantaloupe goes on sale for $1 or less each. One week I might end up at one supermarket, two weeks later at another, and some weeks I won't buy cantaloupe because no one has it on sale. I never buy it at Costco or Trader Joe's because they have set prices rather than sales and never sell cantaloupe so cheaply.
Likewise, I look for grapes (grown in the USA) at under $1 per pound in summer and fall, apples under $1 per pound in the fall and winter, cucumbers for 79¢ or less.
(I have no control over tomatoes or their prices; Papa will buy the tomatoes he wants at whatever price they are. I have in the past suggested less expensive tomatoes than those grown on the vine, or giving up tomatoes when they are not in season, and I might as well have suggested giving up air. This means that tomatoes are something that I have to learn to grow! Cucumbers are like tomatoes; although I do my best to find and buy them on sale, if we need them Papa will buy them at whatever price they are sold at.)
Costco almost always has the least expensive prices on pinto beans, corn tortillas, large Haas avocados, organic carrots, good tomatoes, bananas, frozen spinach, and frozen organic mango chunks. Most of the year they are the least expensive place to buy broccoli.
In summer, the produce stand is usually the cheapest place to buy zucchini, but sometimes the supermarket is. The produce stand is always the cheapest place for oranges because this is a citrus town.
My local Mexican market often has the lowest price on in season produce. Just this week large cucumbers were 4 for 99¢, whereas I haven't seen them cheaper than 69¢ each at the chain supermarkets in several years.
The health food store has ingredients that I can't find other places, and actually has good prices on those specialty items compared to Whole Foods Market. This is where I go for bulk bin grains and legumes that I don't order in big bags from the co-op. They also have Earth Balance in big tubs. In the fall they are the cheapest place to buy organic apples.
I get really interesting things from Amazon. They have good prices on small cases of Bob's Red Mill items such as organic golden flax seeds. I have items for my athletes on my monthly list as well, such as Lara Bars (I could make them but my men don't prefer the consistency and packaging when they are on long rides) along with electrolyte (again, my homemade version didn't go over well). Amazon is also the cheapest place for me to buy chia and hemp seed from.
Azure Standard is my go-to for bulk grains such as wheat, corn, and rice (although occasionally rice is cheaper from Amazon so I always check). I also buy my sucanat from them at prices well below retail.
It can be hard to manage and I'll admit that I can't achieve perfection; I just try to do my best. I focus a lot on the produce prices because that is a big part of the budget and produce prices really fluctuate with the seasons and the weekly ads. This is where I find nit-picking to be really difficult, so having tracked prices and knowing my buy at prices is really helpful. I haven't had a price book for years now, so I need to do that as mostly I compare as I shop and have a good idea of the lowest prices, but not absolute certainty.