#1 - When comparing the prices of two products, look at the unit cost.
This is shopping 101 right here, folks. Here's an easy example using olive oil:
The orange square to the left of the price is showing you how much you'd be paying for a gallon of olive oil at the current purchase price. You'll pay less now for the smaller bottle of olive oil ($6.69 for 16.9 oz), but you're getting a much better rate with the big can ($24.49 for 104 oz) Obviously, buying olive oil in bulk is the way to go, since you're always going to need it, and it doesn't go bad. You're saving at a rate of almost $20/gallon. Every product in the supermarket should show you the unit price, and similar products will always use the same measuring standard. Fer instance, toilet paper and paper towls will use the unit price "per 100 sheets". There are some remarkable differences, but you have to account for quality as well. The trick is to find the best quality product for the lowest unit price.
#2 - When buying packaged meat, vegetables or baked goods, look for the "packed on" date.
Meats, vegetables, and most baked goods are usually packed at the supermarket and can be left on the shelves for days. You obviously want the freshest food, so look for the most recent "packed on" date. Grocers will always put the oldest stuff up front to get rid of it quicker, so you might have to dig around to find the freshies.
#3 - You almost never have to "buy x for $x"
This is usually the old "Buy 10 for $10" or "Buy 3 for $5". What the grocer is not telling you is that you can buy just one item and get it at the same price you would if you bought 10. So, for example, Stop n' Shop says "Buy 10 bags of Doritos for $10", you can buy one and get it for $1. Supermarkets are TRICKY BASTARDS. Look for the fine print: the deal will always specify if you actually need to "Buy 10 for $10" by stating "must buy ten".
#4 - 85% of supermarket circulars are merely showing you the usual price.
Not everything in the supermarket circular is "on sale". Companies pay to have their items listed in the circular, and they are usually at the price you would normally find them at. Look for "with club card" (or something similar) next to the price for the items that are actually on sale. Of course, the "Buy One Get One" deals are the holy grail for deal-seekers, so if any of those items interest you, be sure to stock up while you can.
#5 - The easiest way to save money is to not spend it.
Don't buy what you don't need. Don't buy something you otherwise wouldn't consider just because it's on sale. Don't shop when you're hungry (and chew on some sugarless gum). Consider each purchase - "do I really need this?" "will I actually eat all of this?" This takes patience and diligence, but it's your #1 coupon.