When paying an invoice simply tick the "Auto Rebill" tickbox before submitting payment.
Invoices generated for you will be automatically paid using these card details and the amount credited to your account will be matched against your next invoice.
To update your repeat billing details, the easiest way is either to "credit" your account (this can be anything from £1 and will put towards your next invoice), or pay an invoice before your repeat billing date. Whilst doing this, enter your new card details and tick the "Enable Auto-Billing" checkbox.
Your details will be updated and no more payments will be made on your old card.
All of this can be done from the "Invoices" or "Credit" sections of your Customer Area.