Right now I have to store it on the authorize.net website and then copy the ID back to Odoo, which feels really clunky. There should be a way to add a credit card under the Customers screen.
The other ways is to tell the customer to sign up for the portal -- but that makes no sense while we are on the phone together.
I noticed the http://<odoo>/my/invoices portal has a way to pay an invoice by typing in a credit card, and shows stored payment methods. Not sure if there's a way from that angle.