It is never too soon to start looking for supervisor!
It's not easy and it can take quite a lot of time to find a good adviser so I would give you some advice about it.
First You have to have a clear idea about what would You like to study in Japan.
But don't just think about it - write it (it really makes difference). One page, that's it, about what is the: 1) theme of the research/master course 2) goals 3) tasks to be done during research. Especially think about why Japan and not some other country, what are the potential benefits of your research for Yourself, for Your country and for Japan itself. Anime/manga help you to discover Japan as an amazing country but that's not why you want to go to live and study there. So you have to have a good reason WHY.
Then go through all the Universities (and there is 87 national Universities in Japan) and find
which one has appropriate department that suits Your study program. You will need a lot of time to check all web sites out there and not all of them has an English page.
When You find Universities that suits your interests and concrete departments then you have to look for a staff list
to find appropriate professors whose field of interest matches your research theme/your field of interest. This is also not an easy task as it is usually written in Japanese, but it is very important to contact the right person. Of course you would have to write a letter describing you and your intentions and reasons about studying in Japan, pretty much regular CV and cover letter kind of text.
Then be patient as they will not always response promptly, sometimes it can take two weeks before they answer.
You will probably get a few negative replies, and a lot of no replies at all but don't give up, be patient and keep searching.
You will not always find e-mail addresses of professors on web or their personal pages in English so you would have to try your best to find that info. Maybe mailing University or Department asking them for contact info or something like that.
Good luck guys