You pay for your Registration code from the Products page by hitting the 'Buy' link for the particular program you want (ie Student Edition or Educator Edition).
Payments are processed by a company called Kagi (kagi.com). They accept payment in a variety of ways (Credit Card, Cheque, Money Order, etc) and email you the registration number within 4 hours (in fact, it is usually sent within a matter of minutes).
After you have installed the Evaluation version of Flashcard Suite, you must enter your Registration number to remove the 10-card maximum. You wil receive your Registration number by email after you pay. You then enter this number in the window that appears when you press the 'Enter Number' button (see picture below).
Note: If you do not see this window, quit Flashcard Suite and restart it. It will be the first window you see as the program starts up.