Instructions
Using Xbox 360
Sign in to Xbox Live using your Xbox Live Gold profile.
Select "My Xbox," then move one tab to the right to access your player profile and press the "A" button.
Move one tab to the right and select "Manage Account."
Select "Manage Payment Options." Move one tab to the right to see your memberships and choose "Xbox Live Gold."
Select "Change Payment Options." Choose "Add Credit Card."
Enter the requested information for the credit card that you'd like to link to your account. This will replace your old credit card and make the new one the default.
Using Xbox.com
Visit the Xbox account page (see Resources). Choose "Edit Payment Options."
Sign in to Xbox.com using your Windows Live ID email address and password.
Select "Add a New Credit Card." Fill in the relevant information and select "Save."
Press the "X" button next to your old credit card to permanently remove that card from your Xbox Live Gold account.