Choose carefully where you go shopping: some supermarkets are more expensive than others. Shopping on physical stores is more expensive than shopping online. Don't go for the first price you see on the labels. Search for promotions, try to adequate your demand for products to your currently financial budget in a way you don't spend all your money in the end of the month.
I think this part is the most important when it comes to trying and save more of our monthly income. There are two ways to increase our net worth, cut our monthly expenses or increase our income. When living in a rather poor area of the country with low wages and not a lot of opportunities, then we might not have the option to increase our income. Moving to a better area might also not be an possibility due to external factors. That's why in many cases the only real chance we have is to cut down our living expenses. Especially in the last 12 months with rising food prices I tried to save money wherever possible. Using vouchers and buying in larger quantities helped me to offset some of the price increases. I noticed that some fresh products like vegetables increased 50-100% in price over 6 months in my country, that's insane and won't be able to be paid by the average family for a long period of time. Switching to canned vegetables is not so healthy, but the only chance to save some money. Best would be to start planting my own vegetables, if I had the garden for it.