Run up to Tractor Supply, or Ace Hardware. Both are good places to teach your dog. (ie they do not mind your dog climbing on stuff) Bring a cart to your truck. Ask him to get in the cart, from the bed of your truck. In an amazingly few times, he will associate getting in the cart, with getting to go inside with you. From that day on, the shopping cart will enlist excitement in your dog. This is how things were done before Drive Training came to town.

I suggest using your JUMP command with the dog from day one. We want to maintain a BLACK OR WHITE world for the dog. A confused dog, is a worthless dog. Shades of grey, are only good for confusing a stupid dog.

You will harness this cart excitement, to jump in the cart, WHEN HE IS READY.(Let's use our heads on this on this one) Remember ... if you open your mouth and ask too early, the dog MUST comply. Don't ask too early. The dog will tell you when he is ready. You will see him eyeing up his jump from the ground, and loading up his spinal cord to actually make it. Then you take him to a curb, loading dock, anything that allows him to make the jump easier. Progress asking easier jumps until you have to get onto your dog for jumping into shopping carts, without you first asking.

With those steps, and that association, you can get your dog to jump into shopping carts.

WE ARE GOING TO ASSUME THAT YOU WILL DO ALL OF THIS WITH NO COLLAR OR LEASH. When your dog sees something else that excites him, he will try to jump out of the cart. This is when you must be smarter than your dog, and standing correction ready to teach him better. Take him to as many places as you can, UNTIL he tries to jump out. We do not take anything for granted. He is a stupid dog, that WILL do stupid things. Until you have specifically taught him to stay in the cart, he ain't trustworthy.

Okay now folks, if you have done Drive Training with your dog, there ain't a stick big enough, to teach him self control. It ain't his fault, it is yours'. The way to fix this, is to get out your humane shock collar, and put it around your neck. Hand me the controller and prepare to dance your ass off. LOL
OR
you can get out any of your other humane gimmicks/crutches that you use to control your dog ... be it chain, prong, or even flat collar, then hand me your lead. I have yet to prove this, but I am willing to bet that I can wean you off using any of your gimmicks/crutches, to control your dog.