Make a meal plan/menu- Don't buy food that will expire before you use it. Just because it looks good doesn't mean you have to buy it. Have a plan for all perishables.
Have a realistic budget- If you spend $100/week on groceries don't set your budget at $20/week right off. You will be frustrated and give up. Also, know what your budget includes. Do you use the same amount to buy groceries, diapers, formula, cleaning supplies? Be realistic about what your family needs.
Use cash- This is something I used to be a lot better at. However, after a year of a cash budget I don't typically go over budget. When you know you don't have a credit card to fall back on you are much more careful about what you buy.
Stockpile- When an item you know you will use (but won't expire before you will use it) goes on sale stock up. For example: if you can find a kick butt sale on cereal for say $0.25/box and it is something you know you go through quickly buy 10 or more if you can. Then the next week you aren't stuck buying it at full price. Once you have a good stockpile it allows you to only buy those items for rock bottom prices. Some weeks all I do is stockpile (and milk and produce). I have enough food that really aside from some perishables my family could eat for at least a month. This also allows us the joy of being able to give at times to others in need.
Coupons- A huge part of saving money is to use coupons. When doubled and matched with sales you can find great deals, free stuff, and sometimes they even pay you to take it home. I watch several blogs to help with match ups and I collect coupons from everywhere I go. It is a game to me to see how little I can spend.