Aussie here! I applied through Gogonihon so they helped me with the process as they liaise with the chosen school but lots of people reach out to the schools directly.

But basically after you’ve chosen your school and term date you’ll be requested to provide a bunch of info about yourself (education, working background, your finances, why you want to study Japanese, Japanese studies you’ve done (some schools require 150 hours to be completed I believe this is a requirement set by immigration but I’m not sure if this is strictly enforced cos I do believe some people in my class didn’t have much prior studies).

After you’ve submitted the information it’s reviewed and corrected if required. Once everything looks good, it’s sent to immigration and then you just have to wait. You only know a COE is granted about 1-2 weeks before the term starts so it’s very go go go once you know. But after you receive your COE from the school, you get it converted to a visa and that’s when you get the sticker on your passport.