I do this, and spend about $10 to $15 a week on food, although I suspect the woman was saving up her best coupons for the TV appearance, as it's not possible to use coupons for everything you need to buy. The trick is to match up the coupons with the sales at supermarkets that double them, and you can get items free or nearly so. Last week, I used 14 coupons, and got 10 containers of Greek yogurt for .10 each and so on.
Facebook also has a lot of sponsors with promo pages, and you can get free stuff by "Liking" their pages. The Saturday evening edition of the newspaper has the Sunday coupons that you can clip, without having to buy the big Sunday edition. Being a cheapskate not only saves money, it's a challenge to see how little you can spend.
A supermarket near me sells chicken for .59 a pound, which is unusually cheap. You need to buy this in bulk and make it your main meat item to eat this cheaply. Figure out all kinds of ways to cook it.