When our family eliminated convenience foods and most meats from our grocery list, our grocery budget was nearly halved. We eat a lot of rice, barley, dried beans and peas, lentils, cabbage, carrots, more cabbage, more carrots. We look for "tired" and "ugly" vegetables at reduced prices. Also we grow sprouts in the kitchen, grow peppers and herbs in pots by our back door.
As a constantly hungry college student, I did volunteer work at the local hospital. Volunteers got vouchers for the hospital cafeteria. But this might not be for you.