To add a new credit card, go to the checkout page under "2. Payement method" and click on "Credit card". Enter your credit card information or click. If you already have a registered credit card, click on it and select "Add a new card".
To delete an existing credit card, go to your profile. Under "My payement cards" you can delete whichever credits card you'd like by clicking on the small trashcan on the right.