I spend ~$350 a month for two adults, a 5 year-old who never stops eating, a cat, and the biggest, dopiest Golden Retriever to ever have walked the Earth. This does not include the ~$50 a month for my kid's school lunches, but does include the expensive ass single serve packages of olives that he insists on for snack time at school. Some of the things I do:
Meal planning: This is absolutely the number one thing for me. I have an app on my phone that lets me save and organize all my recipes and it generates a shopping list from the meals I choose. Online grocery ordering/pickup has been a boon here because I can check my pantry and shop for the best price and fit and there's no chance of impulse purchases in the store.
Shopping sales/stocking up on basics: I'm not blessed with an overabundance of options when it comes to grocery stores, but there are a handful of options. I keep an eye on their sales, especially meat, and stock up when the prices drop below a certain point. I do tend to stick to a limited selection of meat types though. Chicken breasts, bottom round roast, boneless pork chops, etc. There are cheaper cuts, especially of chicken (leg quarters are $.35/lb this week), so if I needed to cut down even more, I could. It's also helpful to understand sales cycles. Certain things go on sale, especially as loss leaders, at certain times of the year. BBQ Sauce and Ketchup/Mustard at Memorial Day or 4th of July, sugar/flour/oil/etc just before Thanksgiving. Other things go on sale roughly every three or four months. If you can buy enough (check the expiration dates) to last until the next sale then you won't have to pay full price when you run out. This is where couponing is really effective. One thing that I don't currently do, but have done in the past is keep a price book. Here, Wal-Mart is going to be cheaper 98% of the time for everything except loss leaders and the remaining 2% the difference is so minute that unless there's a LL that makes it worth it, I don't bother (for example, avocados are 30 cents cheaper at IGA than WM, but that would literally be the only thing in the store on my list that's cheaper. It's also way out of my way to go to the IGA, so I don't know if saving $1.50 is worth it.)
Bigger isn't alway better: Before you automatically grab the biggest box of something check the price per ounce/lb/etc. It's not always the better price.
Check the clearance shelf/bump-and-dent section: This takes some discipline to not buy stuff just because it's cheap, but if there's stuff that you buy on a regular basis at a good price stock up (again, check the expiration).
Know when manager's specials happen: At my store, meat gets marked down on Friday mornings, which is convenient because the Friday after payday is my regular off-day at work. Keep in mind that these are on special because they are about to be out of date. Use or freeze immediately. And freeze in manageable portions. I personally break most of my chicken and beef roast down into bite sized chunks, freeze on a sheet tray, and then pack in gallon freezer bags. I can pull as much or as little out as I need when it's time to cook dinner (defrosts faster too).
A little work goes a long way: Things like dried beans are way, way cheaper than their canned counterparts. If you have time on the weekend, cook 4 or 5 lbs of beans and freeze in individual portions. I've frozen beans flat on a sheet before so that they can be stored in one big container and scooped out. They ended up a bit dry, but if you're doing something like soup, it's fine. An instant pot also apparently will cook dried beans fast. Rice can be frozen as well. Brown rice tends to do better than white rice. We don't eat much in the way of carbs anymore, but I would cook large batches of rice in the crockpot on the weekends and freeze for the coming week.
Cut costs on non-food consumables/cleaners: We use bar wipes and cloth napkins instead of paper towels. We've drawn the line at TP, but we used cloth diapers for three years (non-mustachian confession: I bought, off Craigslist, a 1.0 CU portable washing machine specifically for diaper laundry instead of just using the regular washing machine). The countertop guy recommended dish soap and water to clean the granite, and it works just as well on the electric non-smooth-top stove. The floor guy recommended a water/white vinegar cleaner for the floors instead of a specialized "floor cleaner." We've made laundry detergent in the past, but found it rough on our clothes (when you wear the same 8 t-shirts and 4 pairs of jeans every day they get washed a lot). I'd like to revisit that soon. Cleaners and stuff like toothpaste or mouthwash are where you can really save doing the couponing thing as long as you aren't picky about brands. Again, stock up when they go on sale.
There is a caveat here. My spendy pants husband often goes out and buys junk food and snacks. We have separate accounts, so I have no idea how much he spends on that crap in a month, and it's not a necessity, so I don't count it.