The short answer: Eat in season; grow your own; buy in bulk; plan better; reduce waste.
The long answer:
1. Learn to cook well. Not like a few dishes well, which is what many people say you should do, but learn the basics of food science. My mother was a chef and my grandmother a restaurant owner, so a lot of this comes naturally for me, but knowing how to turn an egg into hundreds of possible dishes is an asset. The basics (flour, eggs, salt, butter, milk, sugar) can be purchased cheaply and become a lot of things. I never ate ramen in college. When most people say they "have nothing to eat" in their kitchens, they mean "we have no idea to make due with what we have right now." The modern kitchen is a series of boxes and canned goods with limited applications. I avoid that stuff.
Basically, we try to move up the chain. As food moves further away from its natural state, it becomes more expensive per calorie because each producer makes their money on the value-add. Why buy old pasta or bread when I already have flour, salt and eggs and can make it fresh at a fraction of the cost or, at least, at the same cost for comparable quality?
For example: A whole chicken costs me about $6 from my farmer, but I have to break it down. At the grocer here, you'd pay about the same price for a couple of sickly looking breasts. That chicken becomes several meals, stock and dog treats.
Have a plan for what you're going to eat. I know exactly what I will have in my house at any given time and will have a meal plan set out for the week, often with ingredients playing off one another to maximize their usefulness. Rarely do we stumble outside of our budget because we know exactly what we need.
I'm also comfortable enough in the kitchen to make changes on the fly if we have unexpected company or forgot some necessary ingredient.
2. Gardening and canning. My wife does most of this, which she picked up from her father, a master gardener. We're fortunate enough to have plenty of land in a region with wonderful soil, but you can easily cut down on food costs by growing much of your own food. What we don't eat immediately, we save--and make sure to use. I really despise waste. Anyway, seed costs pennies per calorie and if you're able to save seed, the costs decrease over time, but you have to pay for it in hard work. Some people don't want to invest the time. It's a hobby we enjoy.
3. Forage. This is ridiculous to most people, but when I walk through a park I see dozens of edible things and sometimes I eat them. I grew up spending a lot of time in the woods, so this is another thing that's second nature to me, but I never pay for expensive things that can easily be had for free (like mushrooms and berries like gooseberries, elderberries or raspberries grow wild all around me, along with all sorts of wild greens). I go so far as tapping maple trees. But then again, I'm an adventurous eater.
4. Hunt. Many people don't have the stomach for this sort of thing, but a deer can feed me and my family through a winter and a couple of rabbits can feed us for week. I know this is another ridiculous to people outside the Midwest, but for me it's more about survival a personal connection to food/nature than it is a hobby or a sport. I don't take a lot of pride in killing an animal, but it beats cognitive dissonance.
5. Cut back on meat. Neither I nor my wife are vegetarians (obviously), nor do we want to be, but meat is a luxury generally saved for special occasions or times when there is an abundance of meat, like in the fall when my beef rancher slaughters his cattle and hunting season begins. I honestly don't know if we save money here, since when we do eat meat, we tend to buy more expensive cuts. The price/nutritional value isn't cost effective for us. We eat meats 2 or 3 meals a week, on average. The same way we move up the supply chain for food, we move up the food chain itself. Micheal Pollan once wrote something along the lines of "Eat food, mostly vegetables." That about sums us up.
6. Cut back on calories. I feast a few times a year like most people, but normally our meals are very simple and hit our caloric needs fairly precisely. We're not ones to fret over indulgence, but we do have weight and exercise goals. Everything is measured. Related to #1, we rarely eat second helpings and we rarely have leftovers. I wish I could say we had a methodology here but its really something learned over time.
7. Know your farmers, buy in bulk. This one is harder for a lot of people in cities to do, but I know exactly who's making many of the things in my freezer that I didn't make. I buy organic angus beef from the same man, a quarter at a time, and pay about 2.00 a pound for beef he normally sells for $6/lb in the store. Again, if you're not sure of the basics of food science, this can bite you in the ass because you'll have no idea what to do with all the food. You have to have a plan or you'll end up wasting.
Also, a the kid at the grocery store will look baffled if you try to negotiate prices, a farmer will not, especially if you've known him or her personally for years.
You should look into things like joining CSA, which will force you to eat in season (in turn forcing you to learn to cook strange and new things) and are usually comparable prices to most markets. You can also negotiate on their bumper crops so you can store it.
8. You'll notice a pattern here that I'm kind of forced to eat with the seasons and eat pretty locally (this is what my family's been doing for generations, long before these things became recent trends). This is both good and bad for various reasons. I love ratatouille, but by end of summer I can't stand zucchini. Eating with the seasons, even if you're only shopping at the grocer, means you'll get the food at the best prices.
Winters are toughest here because we don't have fresh produce.
All that said, I like pineapple and citrus and that obviously doesn't grow here in the Midwest. But, I try to buy it in peak season, can and store the flavors into the next season as much as possible.
Most of my food budget comes from buying fresh produce in the dead of winter because I can't stand to eat another canned tomato dish, even though "fresh" tomatoes in winter are terrible. There are also things we just can't get freely or grow here. I could raise chickens, but that's a difficult investment, so I buy eggs from a local market who gets them from a local farmer. I can't use eggs purchased in bulk, so it is hard to beat the price. Milk is the same way. Same with meats that aren't raised locally, like lamb and, annoyingly, pork. Same with things like beans and rice.
Ultimately, I could probably bring those costs down even further, but then I'd be depriving myself and as an epicurean eater, I just can't justify it.
The trade off, or course, is time. I'm super sensitive about time. I can always make more money; I can't make more time. However, I find time savings elsewhere in my life (living closer to my job, don't watch much television, etc.).
It's easy to just pop a frozen pizza into an oven. It takes time to make food from scratch. I'm willing to spend the time in this area because it pays off and beats reading Techcrunch. (Honestly, because we plan and keep it simple, most prep happens on Sundays for the week; 15-20 minute dinners are the norm.)
Anyway, that's the long answer.