JP Bank (Yucho) does offer online banking. It's a pain the butt to setup the first time. I am going to assume you've already filled out the form and gotten your thick packet that includes a folded page with some codes. In the middle is the 初回ログインネットサービス ("first time login service") which is jumble of capital letters and numbers. You will need this the first time you login. At the bottom of the folded sheet, there's a new number that you will need every time you login, your お客様番号 ("customer number") which is a series of 4-4-5 numbers.
You will begin by clicking on "ログイン" from http://www.jp-bank.japanpost.jp/direct/pc/dr_pc_index.html. This will take you to a pointless intermediate page. Scroll down and click "ログイン画面に進む" (advance to login page). On the next page, you will see some really horrific web page design. In the middle, you'll see お客様番号 and a box for 4-4-5 numbers. Fill that in with your info and click "次へ." You will then be prompted to enter your "ログインパスワード" which is on the middle of your page.
Since this is your first time logging in, you will be asked to change your password and setup some security questions ("初めてログインされたお客さまは、「インターネット利用者カード」と共にお送りしました初回入力時に入力するログインパスワードの変更および、画像と合言葉の登録が必要です。まずは、「パスワード変更」をクリックしてください"). Here's where the real fun will begin...
On the next page, there are several boxes. In the top one ("初回ログイン時に入力するパスワード
（インターネットサービス") enter the first-time login password (middle of the cardboard sheet you got). In the next two boxes, enter your password. It must contain at least two English letters and numbers. It must be between 6 and 12 characters. It is case-sensitive (as is the first password they gave you). All of these should be entered as normal Western text (you'll see why I mention this in a moment). In the last box, enter your code that you used when you signed up (申込書に記入したインターネット用暗証番号（注2）). It should be between 6 and 12 characters. Then click "次へ" If you did this right, you will next see "ログインパスワードの変更が完了しました。"
Then click "次へ". Then click it again. Now, you will pick an image. You can take one of those 10 or you can click "別の画像を検索する" to see another random 10. Ultimately, pick one and click "次へ".
The next page is a lot of fun. These are your security questions. But note well -- you need to write them in full-width characters. Ｈａｖｅ ｙｏｕ ｅｖｅｒ ｓｅｅｎ Ｅｎｇｌｉｓｈ ｔｈａｔ ｌｏｏｋｓ ｌｉｋｅ ｔｈｉｓ？ This is what you need it to look like. Or you can enter things in Japanese. All entries must be less than 10 characters in length. Click 次へ. If you did it right, your options will change. First, you should copy that info down. Then click 戻すif is something is wrong OR click 登録する to record your data. You should get a box saying that an e-mail will be sent etc, etc,. Click "OK."
You will now be asked to enter your e-mail address. First screen is just explanation. Click 次へ. On the next screen (enter it normal-style in both boxes) and click 次へ. The click ワンタイムパスワード発行. Then click it again. Now wait for an e-mail. Then enter the part that follows: "ワンタイムパスワード". It should be a number; mine was six digits. Then you will be asked to enter your code that was in the very first form you filled out (the 6-12 digit one) with the prompt "インターネット用暗証番号". Do so and click "実行する." A box will appear asking if you are okay with registering that e-mail address, press OK.
Then click "メインメニュー" and you're in!