First make sure you go with a list so you don't buy stuff you don't need.
Also plan out a weekly menu.
Don't go to the store when you're hungry.
Have a budget and stick to it.
Keep all your receipts and enter it into a spreadsheet.
Because meat is expensive cut back on it.
Cook in bulk and then freeze it.
Cut back on "one-trip" items. You lose a lot on gas and you generally will buy more than one thing.
Stay away from sugar cereals and junk food. They cost a lot with absolutely no nutritional value.
Plan one big trip a month for bulk staples.
Go when the kids are in school. That way you won't be buying lot things you weren't planning on.
Also drink water. Sodas, tea, and fruit drinks cost a lot of money without any real value for you.