I find this time of year my favorite time to cut the grocery budget. There is no beautiful produce to tempt me in the store/market, and naturally frugal, soupy, stewy things seem quite appropriate in February, you know?
My advice: CASH. Yes, lots of people use debit with no problems. Lots of people use credit cards with no problems, with all sorts of benefits. But, in a month where you are really trying to stick to a certain budget, AND that budget is new to you, well, the cash gives you one extra reminder. Impossible to overspend cash, you know? And, for me, it's quite a feeling of accomplishment when I finish the month/week/budget cycle in budget, with only a few cents left.
**disclaimer** I can ALWAYS find something else to buy at the store. Always. So, my grocery budget is my biggest struggle to keep under control. People with more self control/less love of grocery shopping will have different struggles, of course.
For me, when I have a tighter than usual month, I make a list of 2 week or a month's worth of suppers. I aim for a pretty good variety in there. My family's favorite is tacos, so we have Old El Paso style tacos twice a month, we have Mexican (enchiladas, burritos, soup, etc) several times. We have breakfast once a week. And, we have a meatless meal at least once a week (usually something they don't notice--like spaghetti or beans and rice, which they love, or stuffed shells or bean burritos).
I try to plan a lot of those suppers from things I have in the pantry and freezer. If I think, "gee, I need more meat to round out the month", then I look at what's on sale. If it's chicken, I'll add more chicken meals. Beef, pork, whatever. We're not very picky, so anything goes.
I make a list. At the top of the list is things that we really need (want/make life better) to get through the month. So, for us, that's milk (my kids drink it), coffee (LOL), and sugar. Everything else is gravy. Your priorities will vary, of course. Then, I make the list of things to round out my pantry to make all the meals for the month. I try to leave some money for each week, to supplement dairy and produce. I make sure that there are snacks on there. In my family, as long as salsa and chips are in the house, we're good. So, I'll buy 4 bags (a month's worth) at the beginning of the month. They are my dh's favorite, so I just tell him to stretch it, and he does. Also remember drinks (if you drink them), desserts, any special meals (like V-Day), and any times you'll need to take a dish or a meal for something.
In my family, of course we prefer fresh veggies, but we'll eat frozen. We like fresh fruit, but we'll eat frozen and canned (like mandarin oranges or applesauce). So, I add frozen veggies and fruits to the list.
I make a massive shop at the beginning of the month. Buy everything I can at the cheapest store I have available. Then, I divide up the remainder into 3 (for the other 3 weeks). That's the weekly budget for milk/dairy/produce.
This works for me in tight months (though it's not my favorite way to do it), because I know that there is food for the entire month. If, one week, I don't have enough money for salads/fresh produce every night, no big deal, right? We just eat frozen/canned. But, it's usually only 3-4 days until the next shopping day. We can eat anything until then.
For us, that's better than spending most of the money up front, having fresh produce daily for 2 weeks, then realizing we don't get the fresh stuff for 2 more weeks. I'd rather go without for 3-4 days at a time than a 2 week stretch. YMMV on this.