(specials, where to buy what, one brand over another, etc.)
If you're not locked onto a certain brand, you can save by buying what is on special or you have coupons for.
Buying in bulk can be much cheaper, although if it's a product you rarely use or will perish befor you can use it, than it's obviously not worth it.
Always read the price per unit labels on the store shelves to find out what makes the most sense economically. Logic doesn't always apply! Sometimes it's a better deal to buy three small cereal boxes than the one jumbo box...you never know, so you have to do the math!
Sometimes it's much cheaper to buy things at places other than the grocery store --specials at Walmart, the wholesale club, etc. but other times it's much more expensive! It can be a hassle to go different places for different items, but it may save you money. Also, foods bought at convenience stores or gas stations are often much more expensive than at full-sized stores. It's an extra $1 for milk at my local 7-Eleven!
If a product your family regularly uses goes on special, stock up!
If you have a deep freeze, consider buying a cow (or half a cow). You can often get a deal through a butcher or cattle farm where you will be given an entire cow cut and packaged for a nearly wholesale cost.
If you have access to a farmer's market, you can get fantastic deals on fresh produce! Towards the end of most markets, the farmers are willing to sell the product at even further reduction in order to not lug it back home or risk it going bad before the next market day.