How should I try and break into Japan's manga industry?

I'm not the person in Manga field and the following is what I looked into. Hope it helps.
There are mainly three ways to become the manga creator as follows.
Go to the professional school
1) Become the assistant of the professional manga artist
2) Bring directly your creation to the publishing firm
3) Apply to the new face award

Option 2) would be most feasible if you live in the US, I think.

I think what people usually do is to ask one of the manga creator to be the assistant. TO learn how the manga is created in a professional way. create your own story and sell it to one of the publishers.

About 15 years ago, a friend of a friend--both comics artists--wound up doing a series for a Japanese publisher. They approached him, because they'd seen his work and appreciated it. It may be an unusual case, but I think it shows that the best thing you can do is make lots of comics and put them out there in the world. As you practice your craft by doing it, and share it with others, you'll naturally make friends and contacts elsewhere in the comics industry, and comics are a small world, so you never know who you'll meet. Go to cons with your work, get to a point where you're comfortable exhibiting and selling your work, and focus on anime shows, where other exhibitors and guests you meet are more likely to have ties to the industry in Japan. Aside from that, as the other two folks mentioned, I know that apprenticeship and contests in Japanese comics magazines seem to be big ways folks make their break in Japan. Have you tried putting your work up on Webtoons.com? A Korean company, but their service is also very popular in Japan, and you might make some interesting friends and contacts that way, too, plus they often run contests for new publishing deals on their service.
In another question, Camilo, you also asked whether there are any American manga-ka. There are certainly plenty who emulate a traditional manga style, which I'm sure you know. Adam Hughes is the first name that comes to mind, but there are many many more, especially today. Have you read Understanding Comics by Scott McCloud? He has an interesting exploration in the book of storytelling techniques that differ in Japanese manga vs. American comics, and these days, they're also used more and more by western artists influenced by manga.
My advice in a nutshell: Practice your craft, make comics, share them, and make friends of other folks making and sharing their comics!