To get started, head on over to Amazon’s sign in page by clicking here. Fill in the text box with your e-mail address, change the option to 「初めて利用します」, and click on the button highlighted in red to continue.
Fill in the blanks accordingly. Your name does not need to be written in Japanese, so writing in English letters will do just fine. Alternatively, if you wish to write your name in Japanese, remember that the second blank is for furigana (this means write your name in katakana).