How do you approach a customer to inform that their credit card is invalid?

The card machine will simply show either "declined" or "invalid" in most instances. As a merchant you simple hand the card back to the customer and say that your credit card was not accepted by the bank. The customer usually gets very defensive and says that all their bills are paid up, etc. Simply tell them that they need to work out the issue with their bank who issued the card and that there is nothing you can do for them at this point.