1. Log in from https://theone.babymetal.jp/
2. Press [【TOKYO DOME 公演】 THE ONE 限定特別チケット先行スタート！！]
3. Click https://theone.babymetal.jp/ticket/TD.php in red.
4. You have to choose either THE ONE SEAT or MOSH'SH SEAT
Only one ticket of THE ONE SEAT is available for each THE ONE member, and when you enter the venue, you have to show your facial recognition. If you haven't registered your face, you have to register your face at first.
You can buy up to 4 ticket of MOSH'SH SEAT per THE ONE member.
5. If you are ready, press [チケット申し込み].
6. Press 申込/公演詳細.
7. Choose Seat Type (席種/枚数).
第1希望 means your first choice. 第2希望 means your second choice. (You may apply only one ticket type or two.)
Pull-downs on the right means:
席種=seat type (Choose THE ONE SEAT or MOSH'SH SEAT).
枚数=number of tickets. You can choose up to for MOSH'SH SEAT but only one for THE ONE SEAT.
支払い方法 means a method of payment.
Select クレジット(Credit card).
チケット受取り・入場方法*（how to receive your ticket/admission method)
This may be a problem, because this doesn't say anything about a foreign address. The postal cost is 617 yen in Japan, it says.
システム使用料 means system fee.
8. Press 確認(Confirm)
9. Enter your BABYMETAL Ticket会員(member) ID and password.
10. Log in and confirm your order.
(If you haven't become a member, please see the procedure below.)
I hope this will clarify your questions.
To become a BABYMETAL Ticket 会員
1. Choose 新規BABYMETAL TICKET会員
2. Check 利用規約を確認しました and enter your e-mail address.
3. Press 同意する
4. A message will be sent to your e-mail account. Press the URL on it, go to the page and enter information required.
5. After getting your membership return to the above 9 and follow the instructions.
[Note: as I have already made an application for tickets, I cannot go further in the above procedure. Should you have any question, please give a comment and relevant screenshot. Then I can translate it for you. RGDS]