When things get close to their expiration date, they are out of season, or they've been around too long the store will put them on clearance. Stores cannot, by law, sell food items that have expired so the items they put on clearance will generally be good for several days or months. So, be aware of what you're buying and wether you can use it relatively soon.
You can also generally use a coupon with clearance items for an even better deal. I have regularly seen chocolate, diapers, formula, and snack food on clearance at 50% off that I could pair a coupon with and end up paying pennies for.
Clearance sections are generally found towards the back of the store (out of sight) and there may be multiple locations. Get in the habit of checking them every time you are in the store as the good deals change rapidly.
You also may want to check with your grocery store's butcher and find out when they mark down their meats. Most of the meat I buy goes straight to my freezer anyway so if the meat is expiring soon it doesn't really matter.
Buying next years kid's clothing at end of season clearance sales is also a great way to save money. Just keep your eyes open and get a good idea of sizes and what you're willing to spend.
Clearance items are hard to plan for and you generally have to jump on the deal when you find it, but they are a great way to save money.