Shop only on the outside aisles of your grocery store. Less packaging = lower cost.
Think: whole grain breads, lean meats, fruits and veggies, low fat cheeses and yogurts, nuts / legumes and dried fruits. Go "inside" for things like frozen veggies, canned beans, canned tomatos, whole wheat pasta, and olive oil.
When you get home, spend an hour or so wrapping things and cutting up veggies into portion-sized containers; freeze what you won't use for awhile, refrigerate those you'll use right away, and cupboard/pantry things in bulk containers (pasta, rice, etc.)