How do I save money at the grocery store?

First you need to locate all the stores in your area. Anywhere that sells food (I've gotten killer grocery deals at Target!), and then find a blog that does coupon/sale matchups for the stores you have. You can find the Souther Savers blog link on the top of my blog, it is a great blog!

Make sure you get a sunday paper, and have access to a printer. When you go to the blog, it will break down everything on sale, what coupons to use to make it a better deal, and then the final price after coupons. It will also tell you where to find each coupon, it might be an IP (internet printable) or a coupon from your Sunday paper. This will look like this:

Ronzoni Garden Delight pasta, 10/$10 (ten items for $10, a fancy way of saying they are on sale for $1)
$1/1 box of pasta SS 3/27 ex. 6/12 (one dollar off of one box of pasta, coupon in the Smart Source insert of the 3/27/11 newspaper, coupon expires on 6/12/11)
((use $1 off coupon, makes it FREE))

So then you find the best deals in your store for that week, judging by sale prices and what you have coupons for. Buy as many of those items as you can, you want to buy enough at that great price to last you until you can buy it for that price again (usually 3 months). Your shopping trips may look like this:

Week 1-
12 boxes pasta (free)
6 bricks of cream cheese ($0.50 each)
12 bags of frozen veggies ($0.67 each)
6 boxes rice ($1 each)
If you bought these items at full price, it would be around $60. But because of the sales and coupons, you will pay around $17.

Week 2-
2 64oz bags frozen boneless skinless chicken breasts ($5.49 each)
6 bags of shredded cheese ($1 each)
4 boxes pancake mix ($1.50 each)
8 boxes of cereal ($1 each)
Full price $62, you will pay $31

Keep it up an at the end of the month you will have around $240 worth of food filling your pantry and freezer for a total cost of $80-$100.
You just keep going, every week buying those 3-4 great deals and spending around $20 and having it last you three months. By the end of a 6 month time frame, you will be fully stocked to the brim of everything you could want. And you will have spend a very small amount of money to get it.