Not necessarily where you would think of for an afternoon of fun, but it can be done. Not only do you get your weekly shop done, it's educational into the bargain!
First of all, get your small child on board with the idea. Let them decide what to have for tea (M usually picks sausages, or pasta), and write a shopping list of what they'll need. In our case, it turned out to be toad in the hole, so we needed sausages, eggs and milk (we already had flour). M's into writing words, so she wrote the list, and drew pictures of the things as well. I then issued her with a shopping bag, and put £5 in her purse so she could buy the ingredients.
It then helps if you have a small shopping basket, or one of those little plastic shopping trolleys. Sling it in the car, and tootle off to your local friendly branch of Sainsbury's/Morrisons/Lidl etc. Collect your grownup-size trolley, and let your small companion wheel theirs next to you. This should give the staff and fellow shoppers a bit of a giggle.
Proceed with your weekly shop, making sure the small child is looking for the things on their shopping list too. It's excellent for looking for food beginning with a particular letter, reading words on boxes and packets, finding special offers (and explaining why 2 for 1 is a bargain). Don't forget to look at the deli counters for free samples...
At the checkout, let your helper unload their trolley contents and pay using the money you've given them (which hopefully you didn't have to raid the piggy bank for). Load all the shopping into the bag you gave them earlier, and check the receipt (it's never too early to start on this one, plus you get to plug how reading is useful for all kinds of things, not just books). The receipt is strangely popular in our house. Not sure why.
Take your food home, unpack, and then cook your tea (I guarantee this escapade will take all afternoon, and you'll probably be in need of a little something by the time you get back).