Read the labels and compare store brand items to famous brands. They usually cost less and are just as good. Start from scratch rather than prepared freezer or packaged items. Get used to eating meals at home and make it a special family time rather than eating out. Learning to cook simply, rather than rich and fancy, can save a bunch.
Small things can make the food attractive without the added calories and expense.
Don't allow your children to rule the shopping cart. You set the standards and have them help you stick to it. Glean from neighbors gardens. You'd be surprised how many are growing too much for themselves and would welcome a little extra income and someone who was willing to pick and use their extra.