If the stores there have the option to order online and pickup, it will help prevent impulse buying. If possible, shop for two weeks rather than one. Keep a running list of items you run out of, so you aren't running back to the store for forgotten items. The more trips to the store one makes, the more they spend.
Plan trips to do things (grocery shopping, hair cuts, doctor appointments, post office, etc.) in a logical order so you aren't driving back and forth.
Eat more casseroles, soups, stews, etc., that don't require a large serving of meat per person. Eat one or two meatless meals per week.
Avoid buying national brand items and opt for store brand.
I don't pound chicken breasts, but I do split them horizontally, so one becomes two.