There is one absolute best way to spend less on groceries, and it is something that everyone can do, regardless of where you live, what diet you're on, or how much money you have.
What's the secret? When you're shopping, write down the cost of every item before putting it in your cart.
You will be amazed at how your food choices will change. For example, once I started doing this, I shifted to buying fruit and vegetables that were in season (and thus less expensive), rather than just buying things randomly and oblivious to the cost. The same goes for choices of meats, fish, and even non-food household items like soaps, detergents, toiletries, etc.
This is by far the best method of spending less on groceries that can apply to everyone. If you've never done it, I challenge you to try it just once. And if you have any suggestions on how to make this strategy even more effective, please let me know!