If your domain is going to expire at GoDaddy and you need to update your credit card expiration date or add a new credit card, here are the steps you need to follow.
1.) Go to this page:

http://www.godaddy.com

2.) Sign in:

Customer # or Login name: ********
Password: *******

3.) Click “My Account” (upper left)

4.) Bottom right, below “Customer Info & More” find “Credit Card & Payment Info.” You’ll see your credit card info in there. If it’s the same card, but you just need to update the expiration date, you can click the circle and then click “Update payment method” and change the dates. If you need to add a new card, you can do that, too.

If you don’t do this, you could lose your domain name.