I have been poor, and am poor, and your reluctance to accept that really pisses me off. I'm not saying it's easy, because it isn't, but calling me "clueless" for actually having lived in poverty and clawed my way out of it for a while is really insulting. So in conclusion, GFY.
Here's the thing. Yes, it's hard being poor. It takes a lot of hard work and some lucky breaks to get out of poverty. If you are single and can't cook, your ability to save money on the grocery budget is going to be much tougher. Giving credit where credit is due, while my ex-wife had her shortcomings, she knew how to shop and she knew how to cook* and as a result we were able to eat cheaply but well during those long years early in the marriage when we were on WIC and food stamps. It may not have been that exciting - there was a lot of chicken and rice and zucchini and other stuff that could be raised in the garden, to say nothing of lunchmeat and yogurt from a grocery that specialized in salvage and items just past their sell-by date. We bought the Sunday paper to find out what was going to be on sale and clipped coupons like crazy so we could take advantage of double/triple coupon days. That person holding up the line while he desperately riffled through a fat envelope full of coupons? Yeah. That was me. Scored some serious bargains in those days.
The other half of this is that the tools are there for people who want to learn. I don't know if they still do this, but back when we were drawing WIC and food stamps, we got a USDA-issue cookbook which showed us how to maximize the amount of food we got out of our food stamps. You can go to the library or to used book stores or yard sales and get a copy of The Joy of Cooking or the Betty Crocker cookbook or some damn book that will teach you how to cook if you don't know how. There is Walmart, and co-op food deals like Fare Share that make the dollars stretch further.
But if you're single and illiterate and have a baby/young child to drag around? Good luck, kid.
*P insists she really didn't cook that well, but then P is a foodie. My standards are much lower - once I broke her of the habit of cooking all beef extremely bleeding rare, I had no complaints.