For most JETs in Akita, you are paid once a month. Many Contracting Organizations arrange direct deposit to your bank account.
At some point (probably during the winter), you'll get a small slip of paper that has a bunch of weird Japanese that's hard to understand. That's your income statement, and you'll need that to fill out your taxes. In the United States, it's the equivalent of a W-2.
Here is a translation of some of the items on that income sheet.