You can call the customer service helpline number on the back of the card to start a cancellation process. Expect to navigate a matrix of automated prompts and account information before you speak to a banker. Phone conversations are often recorded for quality assurance, so leave the banker in no doubt as to the reason for your call. Explain firmly and clearly that you wish to close the card. Alternatively, you can cancel the card in-person at a branch of the issuing bank.
Some banks enable you to cancel credit cards online. In general, you will need to log on to the banking portal and follow prompts for account maintenance or changes. Some allow you to submit card closure requests via the mail. Send a notarized closure request so the bank has a way to authenticate your identity. Some cardholders submit written follow-up requests after closing an account over the phone. The existence of a paperwork trail protects you in the event of any mishaps.
You should expect bankers to ask you "why" you want to close the card. This information enables the banker to make a counter offer to save the account. If the interest is too high, he may offer to lower the rate. If you don't use your reward points, he may upgrade your account to a cash rewards card. If you're determined to close, turn down all of the offers, and ask for verbal confirmation the account is closed before you end the call.
You can't truly close an account unless it has a zero balance. The bank may close it to further use, but you still have to make monthly payments. If you pay off the balance owed, have the banker calculate any unbilled accrued interest. Your card may have a zero balance one day, but if interest posts the next the account will re-open. If you plan to close the card by mail, pay the balance a month or two beforehand to ensure no interest charges cause the card to stay active.
Closing a Visa makes sense if you're eager to avoid taking on more debt than you can afford. However, card closure can also hurt your credit score. Credit scores are partly based on your credit card balances as a percentage of your available credit. In scoring terms, high balances are bad news. If you close a card with little or no balance, you reduce your available credit. This could hurt your credit if your remaining cards carry high balances. On the other hand, if you keep cards with zero balances open you may forget about an annual fee, incur a late fee and still hurt your credit score.