Children are very impressionable. If they see you reaching for a credit card every time you go out to shop, they will begin to think that credit cards are an instant source of money (they are) but it's up to you to set the example and teach them that when the time comes for them to get a credit card, its balance should be paid off in full every month.
This is a problem that confronts Gen Y parents in particular because we are gradually moving away from a monetary system based on physical dollar bills. Instead, the majority of consumers are more likely to use electronic payment methods such as a debit or credit card to pay for a store purchase. This has its pros and cons but there is one key thing I would recommend all parents do: before exploring credit cards with children, teach them about saving and spending the old fashioned way - with cash. There is much greater regret among children when the $10 bill they were given is spent than if it were simply accounted for via swiping a card. It may be old fashioned, but it certainly worked for me when I was a child!