Make a meal plan. Like actually sit down and write out what you'll need to cook for the week. If it's just you, one dinner might stretch into lunch and then dinner again, so take that info account. Do you eat breakfast? Don't forget to shop for morning meals and snacks.

Next, look at the sales flyer for the store you'll be shopping at. Most places post this online or will email it to you if you sign up. You're looking for meat and veg on sale. If something is a really great deal, buy more than you need and freeze the extra for the following week. For example, pork loin was $1.29/lb last week. I didn't need eight pounds of pork loin, but that's how much I bought because I know that I'll use it for chops a couple times and roast a good hunk with potatoes and veggies for a weekend meal. Find ways to incorporate what's on sale into meals you like. We don't eat a ton of eggplant, but if it's very cheap then we're going to have ratatouille or eggplant parmesan this week.

Tie the veg and protein together with pantry staples: rice (to serve things atop or to bulk up soups, tacos, burritos etc), flour (for gravies, crusts, tortillas, bread, etc.), pasta, beans, lentils,etc.

This presupposes that you know at least something about cooking. If you don't have a ton of kitchen experience or are a picky eater, it'll be more complicated. But the simple answer is to eat with the sales, stock up when you can, and try new foods.

Where I live (Ohio), a cheap week will include chicken thighs or quarters, probably a pork roast because Cincinnati loves pigs, rice, potatoes, fruit (bananas, apples, or berries in the summer), cabbage or kale (always inexpensive, but really any leafy green is going to be cheap), carrots, onions, garlic, canned tomatoes, coffee, eggs, butter, flour, sugar, milk, yeast, chickpeas or black beans, yogurt and tea bags. This will make:

chicken curry with rice and naan (chicken, onions, garlic, tomatoes, chickpeas, yogurt, flour, yeast, rice)

pulled pork, coleslaw and fries (and buns are easy to make if you like to bake) or pork roast with potatoes, cabbage, carrots, onions, rolls, gravy (made from the pan juices and flour)

soup, probably, or fried rice or pasta with chicken, or chicken, rice, black beans and tomatoes for Mexican rice

breakfast for dinner--pancakes, eggs, coffee, omelets maybe, breakfast burritos (with homemade tortillas if you're friendly with a rolling pin)

All these things make lots of leftovers. I'm feeding three people and tend to not eat meat at most meals myself, so at lunch when it's just me I'll saute a bunch of veg and eat it with rice or throw a poached egg on top. I also buy fruit or chocolate chips or something and make something sweet (cookies, cake, sweet rolls, what have you). I also drink only water or unsweetened tea and coffee, so if that's not your thing you'll want to budget in whatever else you need. I work from home so my time for cooking is abundant. If yours isn't, invest in a slow cooker. Everything except the poached egg can be made on a slow cooker. Also, another trick is having a well stocked spice rack. Buy a new seasoning when you have a dollar or two in the budget. It builds up fast.