- they get an EIN (Employee Identification Number) from the IRS, and then
- fill in form W-8BEN and send it to Amazon.
I have just been through this process, and was helped along the way by various posts on forums and on Kindle Boards about how to do it all successfully.
There is a post here that explains it all, and walks you through the process of filling in the form to send to Amazon once you have your EIN:
Do it as soon as you put your book up on Amazon.
(Authors from other countries may also find this information useful; it addresses all authors living in countries that have tax treaties with the USA.)