Here are some of our tips, not that we always manage to implement them:
#1 budget helper: A meal plan based on that week's sales. I pick the store that matches our needs the best and go there, rather than driving all around, but depending on how close your stores are to you or each other you could probably save more. If chicken's a great deal, then I gather up my chicken recipes and go to. It is a balancing act but with practice it helps, especially added to...
#2 budget helper: Learning the sale cycles for pantry/frozen (depending on freezer size) items. Canned tomatoes, for example, go on sale about every 8 weeks, so I try to pick up 8-10 cans when they do (depending on what I have left). Cheese blocks are about every 6 weeks. Flour goes on sale in the 8 weeks before the holidays. I used to budget 10% of our food budget for amazing sales, so as not to go crazy.
#3 budget helper: A bunch of what I think of as "peasant food" recipes. Soups are amazing as a PP noted - you can pair them with so many other things if you feel the need, based on what's inexpensive, and if you either make your own stock or look for deep sales, it's basically made of bits that didn't make it into the main meals. Pea soup is a constant wonder to me - split peas are so inexpensive, throw in one carrot and one potato and one onion and some thyme + stock and you have a hearty tasty massive pot for like, $1.25. A lot depends on your tastes but we enjoy, matched against sales, lentil/onion/rice and other beans + rice recipes, cassoulet-type casseroles, goulash, chili, etc. We adapt them so that the most expensive ingredient (usually the meat) has less and the other vegetables and legumes have a little more. I try to do at least two lower-cost meals a week to keep in practice.
I also have a slew of "effort not cost" recipes for weekends, sort of luxury items that don't cost a lot but time - risotto is the best example, but making fresh pasta or your own stuffed dumplings would qualify. I think of these as recreation to make.
Any recipe that starts with something like "take 6 skinless boneless chicken breasts" is reserved for a luxury meal, which I also try to plan in too, especially when there's a (is this getting boring) sale or we happen to have extra budget that week.
#4 budget helper: Know which days you tend to order in/eat out, find fast & easy alternatives and see if you can implement those. For example, even though I know that whatever they put in them to make them keep is probably horrible, I keep some of the pizza shells you can find (the vacuum sealed ones) around for when it would be a pizza night. Another example is we love to eat Greek food out, so one of our "splurges" is to hit the store on the way home for fresh bread and feta cheese and salad fixings and add in from the pantry good olives, roasted red pepper &/or eggplant, hummus (we make our own usually but sometimes we buy this fresh as well), olive oil, dressing, and then we have a "picnic" with all that greek-inspired stuff, just cold where we top the bread with the veggies and cheese or dip in the oil, have a salad. It is pricier than a more humble/planned meal but way way less than picking it up.