I agree with many of the answers given as viable strategies for saving money. There are a few points that I would add that have saved me money over the years. My wife and I have 7 children, and we have learned that over time our strategy has changed. This is my first point: What once worked may not work in the future. This is because of changes to how stores conduct business, how prices fluctuate, how coupons or sales evolve over time, but it can also change because your family grows (or shrinks in my case), your budget changes, or your time to price compare and drive around town changes.
Time vs Money vs Space
I have learned to be wary when shopping. I own 2 fridges, a full size freezer, and several storage shelves, so I know how to stock up. Stocking up means planning. Don't buy things that you can't use within a reasonable amount of time for your household size. In this equation of savings you have 3 resources to consider. Money is only one of the 3. The other two are time and space. Time is a very valuable resource and how much you have will depend on your circumstances. More time means you can save more money, there is a trade off between the two, but at a certain point there is also a diminishing return, where adding more time to the process doesn't net much cost savings. You will have to gauge this based on what items you like to purchase and your family size. Lastly, storage space is an important commodity, when you use up space in your fridge, freezer or shelves, you have less room for something else to be stored, you have to evaluate how much of any item is worth utilizing the space. Stores do this all the time when allocating how much space and the location of the space is used for any given item, and manufacturers even pay premium prices for more space or more prominent space in a store.
Not all coupons and sales are good
Other areas I am wary in, include coupons and sales themselves, I will not purchase anything, no matter how good the price is, if it isn't something I don't normally consume. I always compare prices based on how much I am getting per ounce when it comes to food. But with perishables, sometimes it is worth the cost to purchase less or to get more expensive items if they are stored in smaller containers that will let them stay fresher longer once opened. Examples of smaller containers include single serve packages of chips and crackers. Along with this is my mantra that buying in bulk sometimes means you eat in bulk, especially with kids in the house. If I have a lot of cereal or snacks, somehow a lot of cereal and snacks will get eaten quickly.
Order Online for Pickup
If your store offers pickup options it saves a lot in the time and money resource categories as well. My wife and I have found that when we don't go into the store proper we save more on our purchases, we simply buy less.
Weigh Store Benefits
I have a few stores that are local to me that have their loyalty cards that have decent benefits. I recently cashed in my points and got several gift cards to Amazon and local restaurants. Another local store allows you to use points to save on fuel costs.
Often store brands have comparable quality to national brands and even when they are not on sale can save you money, even over national brands that are on sale. Be aware that in most cases, things like milk, regardless of the brand, come from the same dairy plants within your region. No need to splurge for national branded produce either. Many of the store brands are packaged in the same facilities that make the national brands. Where I live, the same plant makes yogurts for national brands, McDonald's, Wal-Mart and others, they do the same for other dairy products like cheese.
I have, on many occasions, noticed that sometimes smaller packaged items of the same brand are more cost effective per ounce than the 'family' or other bulk size items. This is uncommon but it is useful to quickly glance at all the prices and sizes of a product. Useful stores will have the price per ounce printed under the total price.
"You could save..."
When I see these words in an ad or commercial for an item, I tell myself, I can save all my money by not buying that product at all. We are talking about managing on a lot of different levels. One of those levels is just being self aware enough to say, 'I really don't need that product'. Don't buy on emotion or hunger or anything else other than your grocery list/menu/budget. If you want to splurge or do something that is out of the norm, that is fine, just make sure you plan it before you go shopping and it is a part of the grocery list/menu/budget.