The procedure will be different for each provider; however, typically a card holder will have to do the following:
Answer) Cancelling a credit card is not as simple as simply cutting the card in half and sending it back to the provider via the post.
To successfully cancel a credit card the account will need to have a "zero balance": which means the card holder will need to have paid off any debt existing upon the account. If the card holder does have a zero balance, then there may be an option to cancel the card online; if the card holder has online access to their account.
If the card holder does not have online access, then the card should have a customer services telephone number on it's reverse: the card holder should phone this number up and there should be a customer service department for handling account closures. The final stage will be cutting your card in half -- vertically -- when the process if complete.
If both of the above options are not available -- perhaps the card holder does not have access online or via telephone due to debt problems -- then a card holder can make a written request: send a letter asking to cancel your account. It is sometimes advised to send written confirmation, even if the card holder has cancelled online or via the telephone.
Cutting the card in half is the final set, and should only be done when the card holder is sure the account is closed; such as receiving a letter in the post confirming the account closure. Cutting the card earlier may be hasty if the request is denied or an error has been made. A credit card has to be cut vertically and not horizontally, when returning it to the card issuer/provider.