What have I done that saves me the most grocery money? In a few words, meal planning. This is one of the most successful strategies that I have tried.
Here's how this works for me. One day a week, I sit down with my family and ask for input for what they would like to eat for the next week. We try to put together menus that include everyone's likes and what they feel like for the next week. It mostly consists of the main course. We usually try to fill in side dishes with what we already have in the pantry or freezer. Of course, if there is a side dish that someone prefers to have, we try to add that. Next, I make a grocery list which includes only the items that we need to make the meals for the week.
This idea to plan meals was foreign to me even though I had read about it from various websites. It didn't occur to me that I could actually do this AND save money until we bought a camper and started camping. With limited space, I had to find a way to take only the food that we needed. I found a wonderful form to use when we went camping (http://www.thecampingjournal.com/PDFs/RV%20Meal%20Plan%20&%20Shopping%20List%20PDF.pdf) and this form helped me to make sure that I had everything necessary when we got there. After camping several times, I started thinking maybe this form or one like it could help me with my weekly grocery budget. All I can say is IT HAS!
Try this for a week and then compare your grocery expenses this week to last week. This is definitely a worthwhile strategy for us.