Plan your meals ahead of time and prepare a list of groceries for the store. Then look for coupons in your coupon holder that you have had already set up.
Show without the children if possible and eat before shopping. Stick to the list, buy only what you need, use coupons and go on full stomach. Buy groceries for at least a full week or more. Shop at wholesale stores like Winco that make you bag your own but save on groceries. Also buy from the bulk bins. Rather than buying Uncle Ben's wild rice I just scoop it out from the bin and bag it. The cost is half of a packaged item.