Easiest way to save on the food bill?
Stop buying the big brand name stuff. That's a biggie, you look around and you'll get store own-label stuff that's just as good, or better, at a fraction of the cost.
Don't take advantage of big flashy "Buy 3 get 1 free" deals unless you know you WILL use whatever is on offer and that it works out cheaper than a store's own-label offer. These deals are one of the worst for creating waste, and you ain't saving squat.
Stop buying pre-made and junk food.
Watch out for deals, especially on meat and fish which can go straight into the freezer.
Look for discounted meat/fish close to sell by date, straight into the freezer with it.
Figure out which stores do the best prices on things. Some are cheaper for some things than others so take advantage of it, don't just stick to one place because it's convenient. I'm off to one store soon, and will pay roughly €40 on a load of stuff we need. I go to a different store then the same things, effectively, in different packaging will cost at least half as much again
Ground meat, whether it is chicken, pork or beef, is your friend. Cheap and can be turned into so many things from a stew to burgers to meatballs to kebabs.
If there's enough leftovers, freeze them. And don't forget that any potatoes that are at least part cooked can be frozen for use another day. Never throw out food that can be frozen and eaten later unless there's not enough for one person.
Make soup. Healthy as fuck, filling, and cheap as hell to make.
And make a list before going to the store, and STICK TO IT, no more "Oooh, this looks nice, I'll buy that" impulse buys.
We cut our food bill in half, we like to stick to around €50-60 per week for two now and that ain't some poor "student" diet, we eat enough and eat decent food which, considering that we have to be on a low-fat, zero-sugar diet means we can't buy the cheaper things like chicken thighs and so on is no mean feat. But with proper planning you buy only what you need, and make as many things as you can so you're not buying expensive pre-packed stuff costing a fortune. A good idea above was the crock pot, and there's so many other ways like the reason I bought a tajine that is WAY too big for two but gives a good rice/veg/meat dish for at least two days that costs very little. We could cut the food bill further if we wanted, but since we have a good variation in what we eat, from chicken to turkey to pork to beef to fish with potatoes/rice/pasta/noodles/wraps/pita/whatever and plenty rabbit food then I'm happy with how the bill sits right now, especially as my regular blood tests are telling me that most things are in order (cholesterol is a little high but coming down quickly, blood sugar in order, mostly everything within "normal" parameters except white blood cell count which has always been high and vitamin D which needs supplements since, being Scottish, is always going to be low no matter what).
You don't need to spend a fortune to eat well, even when you avoid any "white" bread/pasta/rice and go for multi/wholegrain or spelt versions instead of "regular" stuff, and by avoiding certain things and making it ourselves we also cut the amount of garbage so that cost has gone down as well (we pay by the bag. Produce less waste, you pay less). If I had a garden then that would be cut further as any food waste, what little there is but including coffee grounds, used tea, and so on, would be turned into compost instead of being thrown out but that doesn't work in an apartment. Chinese supermarkets are a godsend for things like rice and herbs/spices, you can save a fortune buying there and, well, I do, especially on spices.
Oh, add on another €30-40 per month on cat litter and cat food. We buy everything like that online, a site called Zooplus over here, saves at least 40% compared to going to the stores on exactly the same stuff sold in the stores, the cat litter being the biggest saving there for bloody decent stuff that we get 1+1 free, so that's at least half the cost compared to the equivalent from various stores.
Easy ways to cut bills