You've gotten a bunch of great suggestions here from other posters. I am just going to add a few thoughts...
in addition to buying your groceries cheaper (sales, coupons, bulk, etc), start thinking in terms of cheaper meal ideas. Brand name cold cereal for breakfast is one of the least healthy and most expensive "at home" breakfast meals I can think of! Home cooked oatmeal (not instant) is super easy, quick, and much healthier, not to mention CHEAP! Homemade waffles and pancakes, cooked up ahead of time and frozen... cheap, easy, and healthier.
Lunch meat.... expensive! Leftovers in a thermos (soup, meatloaf, meatballs, pasta, rice, etc) or in a microwaveable glass container... much cheaper. If your family does insist on sandwiches for lunch, try making your own lunch meat equivalents by slicing up turkey, chicken, ham, pork, etc. Also peanut butter and jelly, cheese and jelly, lots of "salads" (chicken, ham, egg). I pack my son's lunch every single day (and did for my DD when she was home as well). DS prefers repetition (plus he is picky and has food allergies), so he gets the same thing 9 out of 10 days. I do buy a nitrite-free, uncured ham "deli meat" for his sandwiches because he has a poultry allergy and it is easier for me to buy him that lunch meat rather than try and find a whole uncured, nitrite-free ham to slice. He also gets the same organic snack bar as a treat in his lunch every day.... bought on sale at Target with coupons when I can find them. But he also takes leftovers when I have something that he likes that is easy to pack.... pizza, soup/stew, meatballs, fried rice.
Dinner.... if you are REALLY trying to reduce your grocery bills you might need to start thinking in terms of some meatless meals or meals that involve meat as a small part of it.....
rice and beans.... super easy, CHEAP, and (IMHO)delicious!
fried rice...... (same as above) and meat can be either minimal or non-existent (although I will use a scrambled egg if I have no meat).
whole wheat pasta and sauce/diced tomatoes. It is important that this be a healthy pasta like whole wheat, especially if you aren't including any meat (or very little meat). Otherwise you might as well give them a Poptart for dinner...

Anyhow, whole wheat pasta can be found on sale and with coupons and is available in bulk at places like Sam's.
eggs.... I can find organic eggs here for $3/dozen and if I use plenty of "extras" in the meal, we can get away with two eggs for each of my men and three egg white for myself.... just barely over a half dozen. I usually serve scrambled eggs or omelets with homemade applesauce (usually with apples that are < 99 cents/lb), and maybe a roasted veggie on the side.... and I suppose toast or a muffin would be good too.
minimal meat meals like tacos..... and stretch that hamburg/ground beef with things like TVP and beans.......soups (my hamburg soup uses less than 1 lb of browned/drained 90% lean beef and serves three hungry folks with leftovers.... and the other ingredients are some of the cheapest produce around like potatoes, carrots, onions, celery canned diced tomatoes.
LAST suggestion would be DON'T WASTE ANYTHING! I try hard for 0% food waste here. Leftovers end up as lunch the next day (and the day after that if necessary). If there is a reason that no one will be here to eat the leftovers, I pack up a container, label it well, and freeze it.... then the next time that DH will be here home alone some night, I pull it out for him and he has a nice homemade dinner for one!
I buy as much organic as the budget allows, scrub them well before peeling, and then save the peelings in the freezer for homemade vegetable stock. When the peelings have been used for the stock and strained off, they go into the garden for compost or (this time of year), out into the yard for the birds and other critters.
End heels of bread that don't get eaten quickly enough get toasted and crumbled and saved in the freezer as breadcrumbs for things like meatloaf.
Anyhow..... to make a long story short (I know.... too late

)..... find some CHEAPER meals and reduce your food waste! Good luck...........P