How do you get your pet(s) to steal things from shops?
All the details are described in this spoiler. The short version is: carry at least one tripe ration so your pet keeps close to you and reward your pet by giving a treat every time it drops something valuable in front of your feet.
Alternatively you can also let your pet fight monsters until it's tough enough to kill shopkeepers, after which you can just take everything in the shop (plus the shopkeeper's money) for free. (Though obviously that takes longer than training your pet to steal if it's still early in the game).