Check the store's coupons. These won't necessarily be in the sales ad, but there may be a bulletin board or a rack near the customer service desk that has the store's coupons. Oftentimes for our local grocery, anyway, they are better than the coupons in the paper.
I don't buy boxed food either (well, I do buy the "kits" - like the rice and spices that you add to your own chicken to make jambalaya or sesame chicken or something like that). Most of the coupons I use are on the other things that add up to your grocery bill. Paper towels, detergent, feminine hygiene, toothpaste, that sort of thing. I have found that the store brand is not always as good, but when it is, I buy that. (Beware of when it's not, however: I tried generic Cheerios once. The baby wouldn't eat them, my husband wouldn't eat them, we took them to the duck park and the DUCKS wouldn't eat them. As they say, the most expensive food, is the food you throw away. Real Cheerios are better, and you can find coupons for those, so yay.) If there are name brands of things that you know you like, then check out the websites for those products. I have had good luck with the Proctor and Gamble and Dreamfields pasta websites, for example, but as for general coupon sites, I have managed to get computer viruses from those. Also, I wouldn't get the paper just for the coupons, but I subscribe anyway, so I might as well use the coupons that are for products I like, since they're there. Between the store's coupons and the coupons from the paper, I generally have about $9/week in coupons. Modest, but I'm also making minimal effort.
Also, if your store's meat section doesn't have a bargain section, just take a step back, and scan for brightly colored tags - the ones at my store are bright orange, the ones at my mom's store are yellow - these are for meat that is going to meet its sell-by date either today or tomorrow. (Find out what day your store restocks meat, and go the day before; you might have better luck.) That is generally what we are having for dinner on grocery-store day. Or, what I'm freezing, or even cooking and putting in the freezer to use later.
I have also found that if I get the store brand's "natural beef" (ie, hormone and antibiotic free) from the butcher counter, it is cheaper per pound than the national brand's packaged stuff. Also, butter and sausage freeze really well - if you find those on sale or with a coupon, buy one more than you need.
Practice some tricks when paying by the pound: At some butcher or seafood counters, you can ask them to trim the meat a little - some of the fat off a steak, or the tail end of a salmon fillet - you pay by the pound, so take off a few oz. Never hurts to ask, right? I have done this at the deli counter, too - if they have to open a new package of deli meat for you, specify that you don't want the first slice - it will be mostly rind or skin or peel - you won't be able to eat it, so why pay for it? If you know y'all are only going to eat five bananas this week, then only buy five bananas. If the bunches all have six or more, snap one off. (This is common practice at our grocery store - the produce department employees will even help.) Or, buy five individual bananas that other people have snapped off. All little things, a couple of dollars here and there, but it adds up eventually.
Happy shopping!