As far as my grocery habits, I put what I need into my grocery app, as I realize I need it. (I am LOVING the 21st century!)
As much as possible, I go over the shopping cart, delete anything I don't really need, and pull the trigger on the order once per calendar month.
If I forget something, I live without it until next month. Part of this is practice, and part of it is that there is a charge for grocery delivery, no matter how large the order (no free delivery) - so I don't want to place an order (and pay the fees) because I forgot a few items.
This is the start. As you get used to (train) not going to the store every week (or day), that is the beginning of your savings.
How?
The less time you spend in the store, the less money you spend. EVERYTHING in the store is designed to get you to spend more money than you had planned; from the colors and layout, to the junk lining the checkout aisle. Even stores where it looks like stuff is thrown on the shelves willy-nilly, there's a plan behind it to get you to spend on impulse.
Example: we've all had the experience of going to a grocery or dollar store for ONE thing, and planned to pop in, get it and go... So, you don't need a basket or shopping cart, right?
As you check out, and take your shopping bags (!!) to the car, you vaguely wonder what happened to the 'get ONE thing' idea, lol.
There's more, but this is the start.
TL; DR: Make a list, and plan to stay out of stores as much as possible.
If once a month is too long, due to space or money constraints, work on going as little as possible, and extending the time between trips.
There's more, if you're interested. When I spoke to Ben this week, I realized I started doing this back in 1993(!), and I lot of what I do now I don't have to think much about it.
So, if you're interested, I will break it down as best as I can.
Ben Jason Dawn Shauna Kim