I do not know how a family of 5 can budget 100/week. Some of these replies must do things I don't know how to do either! What I do is this: I live where all these stores are VERY close, so that helps, but I look at the sales papers that come in the mail every week. I go through and write down what sales are at what store that I would be interested in, and then compare to decide where I'm going (Albertsons, Kroger, or Tom Thumb). There is a basic inventory that never changes in my kitchen (milk, cream of whatever, onions, etc). Then using the coupons in my purse sized file (which you can get in the office section at Walmart--I made my tabs food, bath, cleaning, going out, baby, etc and put coupons into each section), I make a weekly menu, add a couple days "just in case". I make the menu according to what coupons I have, what we already have at home, and what's on sale. That makes the shopping list pretty basic and then I go to Walmart for the basic stuff (toiletries, cleaning supplies, and canned goods, etc). Then we'll swing by one of the grocery stores for meat (not just for the price but b/c the quality is better), and whatever else may be on sale there that is on my list.
DO NOT BUY PRODUCE AT WALMART. It's sometimes twice the cost, not a good quality at all, and goes bad way too fast. I've thrown money and fits at Walmart produce for the last time. I have to go to the doctor every Monday for bloodwork, and pass right by Sprouts farmer's market on my way home. I do my "real" shopping on the weekend, but my produce shopping I do on Monday at Sprouts: whatever is on sale that week. For example, grapes are $1.99 everywhere right now, but Sprouts has them for 77 cents! Apples are 1.29 instead of 1.99. We do not believe in doing without or eating foods that aren't good for you just to save money. We don't do without at all. But at least on my schedule, we don't spend extra money on gas even if it is 3 stores (just make them preplanned and go when you're going to be near there anyway): we have a 2 year old and 2 parents and we spend $120 every week on food and household items. This may be $140 one week and 100 the next, but we keep the cap on $480/week and we eat out only 1x/month (not included in the grocery budget-we put that in recreation). Another tab in my coupon file is for receipts, and I keep those each week to make sure I'm on track and not accidentally overspending. I empty it every week before going shopping again.
Edited: In all fairness, this does not include diapers, which is about $50/month for wipes and diapers (giant value box of wipes at Walmart, the biggest boxes for the best prices of diapers, at least Pampers, is at Babies R Us).