My basic strategy is to check out the Hy-Vee weekly ad online before I write my grocery list, then make a menu (with cookbooks and www.kraftfoods.com to inspire me). Finally I make my grocery list.

The main thing I do is get Hy-Vee brand for a lot of things. Basic products, like dairy and pasta really don't seem to have that much, if any, of a taste difference. And they are almost always cheaper.
Also, for produce and cheese, I buy the things that haven't been prepared for me. Anytime I buy carrots, celery, lettuce, cauliflower, I buy the kind that still needed to be peeled and chopped (very rarely is it cheaper to buy the pre-chopped sort). I often buy cheese by the block as opposed to the shredded/sliced. It's almost always much cheaper. But sometimes not - today the shredded was the exact same price per ounce as the blocks of cheese, so I got shredded for the kinds of cheese that I needed shredded ultimately anyway.

Another thing that helps out is remembering the prices and paying attention when I'm ringing up. Hy-Vee has an amazing thing called a scan guarantee - if something rings up at the wrong price, it is free. But you have to notice it and point it out, of course. A while back, Clint and I got 4 free frozen pizzas because of the scan guarantee and today I got a bag of shredded cheese for free.
I would like to get better at coupon clipping, but every time I try it, I don't find a lot and even when I try to use some, the off-brand is usually still cheaper than the brand-name with the coupon.
I will say, though, that there are a few things that I have found that are, in my opinion, not worth skimping on. Toilet paper, cereal and deodorant are the main ones so far.
If you have anything else I could do to save money on groceries, let me know.