First, click "My Account" in the bottom left corner of the screen.
From there select "Payment Details"
You'll see any currently available payment methods and you can click "Add New Card" to add another payment method.
Enter in the credit card information for the new card. The Cardholder's Billing Address form can be found by clicking the little map icon.
Fill out the complete billing address information and click "Save Address".
Finally, to save your new card click the "Save" button but ensure you set the new card as your default payment method by checking the circle if you want to delete your old card from available payment methods.