1. Pick what stores to go to. Some stores charge more for the same product. Aldi, for example, buys a lot of generic stuff in bulk, which makes prices on most things significantly cheaper. Farmer's markets also often have cheaper produce because the food is local and the middle man has been cut out.
2. Make use of a frequent shopper card, if available. Stores like Kroger and Giant Eagle have frequent shopper cards, which will often get you discounts per shopping trip, as well as points to use for other things, such as fuel discounts.
3. Buy generic when feasible. I don't just buy generic to buy generic, though. Look at the ingredients. Sometimes, generics will have a lot more preservatives or filler, but in many cases, they'll be exactly the same as your name brand item. When that's the case, buy the generic.
4. Don't go hungry. Going shopping while hungry increase the chance that you'll make impulse buys. Grab a bite to eat before you shop, to prevent that.
5. Buy only what you need. If you're strapped for cash, don't go after that pack of Starbucks Frappucino or that extra sirloin steak. Get just what you need.