Bumping this thread because I'm making an effort to cut down our grocery bills.
The simplest tip I'm discovering is, find out what the specials and "loss leaders" are each week and build the menu around those, at least in terms of produce and meat. In my area, grocery stores come out with the new weekly ad each Wednesday. You can look them up online in advance and plan out the menu, and print off store coupons, if they are required. I'm not organized enough to plan on the fly, so it's better for me to do it in advance and have a list in hand when I enter the store. I have two main stores that I'll shop at, which are very close to each other so I'm not wasting gas driving all around town.
The other tip I'm using is to see what staple items I already have on hand in the kitchen and incorporate those (i.e. canned beans, pasta or couscous, rice, frozen chicken breasts, etc.).
Those tips sound super obvious, but it really adds up, and I'd never had a good strategy before. This week, I spent $70 less than last week! I hope to keep up the trend.