At the moment it is not possible to change your credit card info directly, so what you want to do is cancel your current subscription and then re-subscribe with your new credit card. You won't loose any data.
Step 1: Unsubscribe
Go to your account page through the menu at the top right.
On your account page, find the button that reads: "Cancel subscription" to cancel.
Step 2: Sign up again
After you unsubscribed you can still use your account for the days you already paid if you cancel in the middle of a cycle.
If your subscription has already run out you can just sign up again by picking a plan:
If you still have some paid days left you might want to wait until your subscription runs out so you don't pay twice for the same days.