What do you have to do?
Log in to Adobe, and create an ID (which is very well described).
After creating the ID you are registered as a customer with Adobe (you have already done, if you have for example, loaded a trial version).
You now need to simply open a support case, in which you enter the serial number that you received from Amazon.
As I entered the invoice number Invoice number of Amazon. So there's not a double-form or an extra page where you can get the serial number, but you can do this easily through a support request.
I hope this hint helps.