Setting this up is pretty straightforward -- you'll first need to link a Walmart account to your Google account. Once that's done, you can ask Google Assistant to order whatever item you might be interested in. The Assistant will read you back options that you can accept or decline and it'll tell you what retailer they come from as well as how much they cost. If you specifically want to order from Walmart, you can say "order dog food from Walmart" and it'll only offer you options from that one retailer. Once you've placed an order, you can just tell the Google Assistant to "re-order" whatever you're looking for and it'll just re-buy whatever you picked up last time.
Walmart joins CostCo, Target, Bed Bath and Beyond, Walgreens and a whole host of other retailers available in Google Express. It's not quite the unified shopping experience you get when using Amazon's Echo, which obviously has access to the retailer's massive selection of goods. But given the many Express partners, there's a good chance you can find what you're looking for with Google as well.