After having some trials with my kids at Walmart over the years, some things have started to click for me...
I walked out of the store on a few occasions early in my parenting, and tried using rewards for awhile. This became depressing when they would not often measure up to my specific instructions (ie don't pick things up, or stay near me), and I would not often receive the intense pleasure of rewarding an obedient child. So, I came to the conclusion that giving instructions beforehand seems to be counterproductive, because the children tend to feel a burden and become discouraged. It is far better to give specific instructions as needed, and make sure that they are obeyed at that specific time (a neck squeeze does wonders!).
Secondly, involving the children with the work of shopping gives them something to occupy their thoughts and it makes them feel useful and important (today David minded the list, Deborah steered the cart, and everyone retrieved things we needed within their reach - except Joshua, though he tried:-). This leaves less attention for them to quarrel among themselves or be distracted by things in the store.
And lastly, my attitude is of paramount importance! I've found that if I smile often, the children think I like them (I'm happy to report that I do - most times!), and they like me back. This makes them want to please me and behavior problems become less of an issue.
Also, shopping is a perfect opportunity to homeschool. Today David figured out some hard math questions I asked him about how much cream cheese to buy - we needed 2 1/2 pounds - for Daddy's birthday cake. :-) I remember seeing once a well turned out lady in Walmart with her 4 children. The youngest was maybe 4 they were about 2 years apart. She walked calmly through the store and the children walked sedately beside the cart, two holding onto one side, two on the other. I saw them several times and each time they were just as calm and orderly! Maybe someday I'll have it that together, but until then, I have something to reach for:-)
God is so good to have given us sweet children to train us up in the way we should go. Then, Lord willing, they follow ;-)