First, sign in to Slate at Then go to your account settings page. You can get there by selecting Account from the top right corner

Then click Subscription & Payment..

To update the expiration date, postal code, or security code on an existing card number,  select Edit. 
To change your card to a new number click Add card. To switch to PayPal, click Add PayPal.

If you see your card information, but you are unable to edit the card number and would like to, please return to the account page and click Add Card rather than Edit.