I applied for Amity online and from outside Japan.
Within about a week I was offered a one-way interview. You go to a website and answer about seven questions (though only five are real questions). Your answer can usually be between one and two minutes, if I recall correctly, and you are given multiple attempts to answer the question. These questions are fairly easy; just be upbeat and show that you can speak clearly and you'll probably pass.
Within another week I was offered the first personal interview. I had about two weeks to prepare a demo lesson. They give you the structure they want you to follow, but the lesson material and targeted age level are up to you. The interview lasts about thirty minutes. You'll answer some basic questions about yourself and prior work experiences for ten minutes or so and then do the demo lesson. If I recall correctly, it needs to be ten minutes as well. After this you'll be given a few minutes to write down some self-feedback, and then discuss the lesson with the recruiter. Finally you can ask any questions you have and are given some information about Amity. Even with some pretty bad technical difficulties on my end, I was able to pass this interview, so I assume that as long as the structure of the lesson is good, they don't care.
You'll have about two weeks between the first and second personal interview. One thing to note, as well, is you need to watch some videos at some point -- I forget if they're before the first interview, the second, or if they come later.
My second personal interview was with the head trainer. You will do the demo lesson early into the interview, and then you'll answer some general work questions. You'll also do the same feedback thing regarding the lesson, as well as talk a bit about Amity's general lesson structure. The e-mail implied the interview would be ninety minutes, but for me is was done in about forty-five or fifty.
If you're successful, you'll probably find out pretty quickly. After accepting a position with Amity, I found out where I would be located within about two or three weeks. Before going to Japan, you'll have to take several quizzes and do a couple online calls as well.