If a members is on a plan with no recurring billing (ie: admin or a non recurring plan) then there is no credit card data on the member profile page.
A member who is on a recurring billing plan can go to page /members/75.cfm on your site and when they confirm their password, their c.c. info is there for them to update.
You can also edit their information via "Edit Member Details". If they are on a recurring plan, there will be a place for the credit card information to be entered. When you enter it there, the member will be retried on the new renewal date for them.