Make a meal plan and then a list of the ingredients to buy.
Shop at discount food stores or buy store brands whenever possible. Also check the local deli to see if any soon-to-expire foods have made it onto the rack.
Don't go shopping when hungry.
Buy in bulk. Especially cereal if you have a house full of cereal killers. Bagged cereal is much cheaper than boxed cereal and even some brand name cereals are starting to offer big bags.
Buy fruits, cheese, nuts, and seeds for snacks. Or bake your own snacks.
Prepare your drinks, snacks, and meals for work or school at home. Eating out and vending machines can add up very quickly!
Prepare more homecooked meals. Sites like AllRecipes.com have a wide variety of recipes for every meal, occasion, and time available for cooking.
Buy a deep freezer to store lots of frozen food.
Refrigerate or freeze leftovers that can be eaten later.
Buy or hunt your meat, or pay somebody to do that for you. The deep freezer really comes in handy for this.
Plant a garden if you have the room and time for it.
Infants
Create your own baby food by steaming fruits and vegetables, and then slaughtering them with a fork or in a blender. Many babies go bananas for bananas, which is unsurprising because we are primates. Be cautious about grains though, and don't give a kid under one year old any honey, nuts, peanut butter, milk, or seafood.