Watch the ads for sales and coupons.
Do you have Meijer stores by you? If so, look at mealbox meijer, they have printable coupons that along with store sales have come up with getting food free or almost free. (pasta was on sale last week 2/$1 and they had coupons for $.50 off a box of pasta.
Go to HotCouponWorld and look at the forums for stores near you and what other people are getting for pennies.
Shop your pantry and freezer first. If you don't have an inventory, pull out everything you have wherever you stash food and write it all down. Then start planning on what you can make from what you have. After that figure out what you can make by only buying 1 or 2 ingredients. I've done some odd combinations, but I can feed us out of our cupboards and freezer for at least a week.
Get a 10lb bag of potatoes (or whatever size is on sale). They are cheap and versatile. Bake most of them up. Use some as a side dish for a meal, use others as a baked potato bar to stretch left overs, make twice baked potatoes, chop them up with a little onion and fry with a little oil or butter for breakfast. Use the others for mashed potatoes. A tiny bit of meat, lots of gravy and some veggies to round it out won't cost much.
Go to the $1 store and see what they have in their food section. Sometimes I get really good deals, other times it's a bust.
Look for Aldi, Sav a lot, Big Lots, scratch n dent or salvage grocery stores or amish grocery stores. You can find some good deals there. I just got a Zatarrans rice mix for .65. They are always too spicy for us so I add extra rice and a half a bag of frozen corn and it feeds us for a couple days, but we're a smaller family.
There is Angel Food Ministries. They sell food to anybody, there is no income restrictions. A box of food is $30. Sometimes it's pretty processed, other times it isn't so bad. For another $15-20 you can also get extra boxes of either meat or veggies.
Lastly, there are food pantries and such and while most people don't want to use them, if you can't feed you family or you have to choose between $ for food or paying your bills, there is no shame in getting a little help.

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