Start with the six staples. Rice, beans, pasta, bread, eggs, potatoes. Beans include all sorts of beans (red, black, split peas, chili, garbanzo / chick peas, lima, etc). Bread can be made yourself and is the best thing ever. $30 a month.
Next, add your vegetables. Whatever is on sale at the store. Broccoli, peppers, etc. Also, you have your vegetable staples: onions / shallots / garlic, which make everything taste btter. $30 a month.
Next, meat and cheese. You generally want less than the average american... so, let's say $30 a month, which gets you a family pack of pork chops, chicken thighs, chicken breasts, and some cheese.
Finally, your "whatever". Nuts, candy / junk food, cleaning materials, blah blah blah. Let's call that $30.
Let's be generous and add an occasional cheat of eating out, for $30.
Total: $150, or less than half of what you were eating before.
Now, let's make things a bit more hardcore. You might notice that if you actually spend $30 on staples, that's just... way too much food. Way too much. So let's cut that back gradually to $15. $15 buys you, in the bay area (not cheap!): 10 pounds of potatoes, 5 pounds of rice, 3 pounds of beans, 3 pounds of pasta, two dozen eggs, and enough yeast and flour to make a bunch of bread. Next, let's reduce meat and cheese a bit to $20, you'll thank me for it. $30 in vegetables and fruits means something probably rots, so let's cut that a little until everything gets eaten - $25. Now let's add some vegetables like yams, squash, and some frozen mixed veggies for when you're too lazy to dice; this reduces other vegetable cost because you can only eat so much. $20. And reduce your "whatever" category to $20, and your eating out to $20, and you now have $15 + 20 + 20 + 20 + 20 = $95 a month.
By comparison, I live on $30 a month for food, 1400-1600 kcal per day. Priorities are elsewhere, I don't do it out of need. I spend more on liquor than groceries.