Do you know anyone (or anyone who might know anyone) in the military? Ask if they shop at the commissary, and if they could call you before they go so they can take you along. Food is very cheap there.
Buy family-size packs of meat and separate them into small bags when you get home.
Look for small family owned grocery stores. They generally have vegetables and fruits much, much cheaper than regular grocery stores. For example, I bought a whole bunch of bananas for 21 cents a pound...
Another option are foreign shops, Spanish, Asian?
Don't make a shopping list. Go to the store and look around to see what's cheap.
Contrary to the advice to find vegetable protein, I find meat is a lot cheaper. Meat keeps you full longer than vegetable protein.
You could easily go through $7 worth of vegetable protein and be hungry 2 hours later, when eating $2 dollars worth of meat would keep you satisfied for 5+ hours.
If you are really, really short on cash, don't buy fruit! It will be a waste of money; prioritize meat and vegetables!
Check if there are any social clubs around you (generally for people with health problems). They generally have an afternoon meal for a ridiculous amount like 1 or 2 dollars. Google something like YourTownName social club.
Remember that while meat and vegetables are more expensive, they will keep you satisfied much longer (5+ hours) than empty calories like pasta or bread or pretzels... (1+ hour?!)