Shouldn't you ask someone who is in Japan? A very high majority of the members here are not members because they live outside of Japan, so most everything is a guess as to how exactly you go about joining.

However, the page you linked listed the steps as follows:
1) register with a valid email
2) if the email is valid, you will receive an email with steps on how to join
3) follow the directions in the email
4) you will receive a mail regarding payment
5) within a week of payment, you should receive a hard copy of the bill for joining
6) pay the fee (a yearly fee)
7) after paying, you should receive a Team Ayu confirmation letter
8) you should start getting Team Ayu mailings in about a month