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To do so, you can either press the "Power" button in the front of the console, or press the PS button on a connected controller. You'll need to turn on the controller either way. This will log you into your PlayStation 4. It's one tab left of the Home Screen. This option is at the very bottom of the menu on the left side of the screen. This is the password you use in conjunction with your PSN email address to log into the PlayStation Network. As long as your password is correct, doing so will take you to the "Payment Methods" page. This option is at the bottom of the page, below any other payment methods here. This information includes the cardholder's name, the card number, the card's security code, and the expiration date. It's at the bottom of the page. This should be the address to which the card is registered (e.g., not necessarily your home address). Doing so will add your card to your PlayStation Network account. Now you can select this credit card for purchases at the checkout screen in the PlayStation Store.

Summary:
Turn on your console. Select your profile and press X. Select PlayStation Store and press X. Select Payment Methods and press X. Enter your PlayStation Network password. Select Continue and press X. Select Add a Credit/Debit Card and press X. Enter your card's information. Select Next and press X. Enter your billing address. Select Save and press X.