If you ever need to update your payment information, there's only one link you need: the one that links to your Billing dashboard. From here, click Edit Payment Info, and in seconds, you'll be right where you need to be (i.e., you'll arrive at the page shown below 😉 ).

From here, you can update outdated credit card information by clicking the 'change credit card' hyperlink, then fill in your details, hit save, and voilà 💃

You've saved a new credit card to use for every future transaction.