My girlfriend and I on average spend 30-40 euro's a week on groceries. This is below half of what the country's average weekly shopping budget is for 2 people.
Are my girlfriend and I frugal? No. We're also not even broke or anything. We just happen to have found a 'smart' way of doing groceries.
The best thing we changed in our routine is to plan our meals for the entire week. On monday we do the grocery shopping and we have a meal plan for every day of the week. This helps us to have a clear overview of what we need to buy and also lets us combine ingredients for multiple days. It also helps to buy everything at once, compared to daily grocery shopping. I've found that we were spending a lot more when we did daily groceries, oftentimes at least doubling our current weekly budget.
We also buy things in bulk. When we buy rice, we will buy a big bag of at least 2kgs which will last us weeks. It might seem excessive to buy large quantities of stuff if you don't know what you will eat for the next few weeks, but in my experience it's far cheaper than buying new things every week, in smaller sizes.
Eat green. Going vegetarian or even vegan can be a touchy subject in ML circles, as some comrades find it very privileged to be able to go vega(n). If your idea of vega(n) is the Wholefoods Californian Hipster type, then you might be right. But a lot of cultures around the world are already partly or completely vega(n) and there's a lot of things we can learn from their cuisines. Eating meat in my eyes is a privilege and meat in The West is heavily subsidized to make it cheaper than it should be. Still, cutting meat out of my diet greatly lowered my weekly spendings on food. Meat is expensive, and the alternatives (lentils, beans, soy, tofu, seitan etc) are almost always far cheaper and probably healthier. Going vega(n) is not about changing the piece of meat on your plate for a plant based meat option, it's about changing your entire view on your diet and being open to other cultures and their cuisines.
Routine. I have accepted a routine for my breakfast and lunch which I rarely change. I have been eating the same things for breakfast and lunch for more than a year now. It is nutritious and helps me with my gym life, and it's cheap. If you find meals that work for you, sticking to it can really help you with reducing costs. My breakfast and lunch combo costs me 1.50-2 euro's a day max, and I never get tired of it. Having this routine not only saved me money, it saved me time and it allowed me to have a healthy base to build upon. I also don't have to think about what to eat that much.
Discount shopping. Supermarkets around here have weekly discounts that change every week. It's a good strategy to look what will be in the discount section for the next week and to add it to your meal plan. It can save you multiple euro's each week.
Don't buy brands. Another really big thing that helped me cut spending is to stop buying brands and focus on the cheapest option in the store. I used to drink lots of soda, mostly name brand, and that alone takes up a big part of your budget. I only drink water or sometimes lemonade these days, but if you have to drink soda, buy the cheapest option. The difference in taste is often minimal and your just paying for the name anyway. This goes for a lot of things. Store brand stuff is oftentimes as good as the name brand one, but can be several euro's cheaper.
Be consistent, not perfect. Don't be too hard on yourself if things don't always work out. But be consistent. Have a plan and stick to it for at least 80% of the time. Find out how much money you can spend on food and how much you're willing to spend. And stick to it. Withdraw the weekly amount in cash if you have to, so you can physically see what you have left to spend. But stick to it. That's the important part.