Buy in bulk.

Buy lots of dried beans, rice, etc. (living in earthquake land, I like to keep our canned goods fairly stocked and just rotate out old ones only).

Buy from farmers markets when available, frozen veg when not.

Buy whatever the supermarket is trying to get rid of. In Japan, I end up with mystery seafood a fair amount, but just about anything is fine fried or in a stew.

Stay away from things out-of-season and pre-prepared foods.

Use any space you have to grow something. Even in my Tokyo apartment, I was growing herbs and chilis.

The above helps. I think everyone has some thing they don't want to give up and that's fine. When I first got out on my own in the US, I ended up surviving off of whatever I could get at the restaurants I worked at and boxed, instant mashed potatoes from the dollar store.