How to Change Your Credit Card Number for Windows Store Purchases

From the Microsoft Account: Commerce Website

1. 
   Visit the Microsoft Commerce website.
2. 
   Sign into your Microsoft Account with your Microsoft Account credentials that has the wrongly-entered card number/billing details.
3. 
   Look for the "Payment options" link from the tabs at the top of the page, and click it.
4. 
   Look for and click the button/tab to the credit card you'd like to change. You'll find these tabs over on the left side of the page.
5. 
   Click the "remove" button to remove the card from your account, if the card number itself is incorrect.

   1. You can still get away with editing all the other details of your credit card(such as the expiration date or other billing details of the card, without removing, and instead click the "edit" button.
      
6. 
   Set up a brand new billing credit card from the billing options area on the Windows Store. As of right now, the Microsoft Account Commerce website, doesn't have an accurate way to add a new credit card to your account without going through the Windows 8 Store.