I know little about grants/scholarships for international students. But an overview of the Japanese graduate schools and grants/scholarships for Japanese students is like this:
Masters programs (excluding MBA, law schools, etc.):
Students of liberal art major including some of soft science such as social science rarely go to grad school. But probably more than half of engineering and hard science undergraduate students go to grad school, finish masters programs, and often look for non-academic jobs. The rate of going to grad school varies depending on the discipline and university. In general, practical areas and universities with excellent undergraduate education have a higher rate, and pure science like math and smaller universities have a lower rate.
Whatever your major, financing is abysmal. You might be able to work as a TA, but that's far from enough to support yourself. The wage rate is pretty much the same as your average part time job, and you can only work for several hours at most in a week. In many schools there is no tuition waiver even for engineering and hard science majors. You have to pay the full tuition unless you're qualified for a special program for working students in severe economical situations.
Labs funded by large grants will support your research expenses such as traveling expenses to attend international conferences. They might partially support students by hiring them as RAs. But as far as I know, wages are pretty much the same as TAs.
There are private scholarships and the like. Your school might have its own scholarships too. But these are exceptional cases.
There are various student loans, and quite a few people take advantage of the lower interest rates.
Some schools offer excellent masters programs, and others don't. While Japanese universities are notorious for their ridiculous entrance exams, grad schools are much less competitive.
Ph.D. programs (after masters courses):
Pretty much every program focuses on training researchers. In fact, there are few career options for Ph.D.s outside academia in Japan.
Again, level and quality vary greatly from school to school and from field to field. And you don't need to worry about the competition. Because you're supposed to be a would-be researcher/professor, you're going to compete with geniuses from all over the world sooner or later anyway.
The most popular scholarship/grant for Ph.D. candidates is
the JSPS research fellowship. If I remember correctly, non-Japanese students can also apply for it. As the table says, the salary is 200,000 yen (about 2,200 us dollars) per month. You can also apply for a research grant up to 1,500,000 yen (about 16,500 us dollars) per year.
In mathematics, most likely you can get the salary and (part of) grant if you've published a paper in a peer-reviewed journal published by a major publisher like Springer or Elsevier before you get a master degree. Less prestigious peer-reviewed journals might work too. If you haven't published anything, it's hit or miss. Of course, different fields have different standards. But I kind of doubt there is a field where a relatively good student is supposed to have published multiple papers in good journals during their master education. You can apply for it after getting a master degree, but the standards are higher for obvious reasons.
The wages for TAs and RAs are pretty much the same as when you're a master student.
In math (pure and applied) and computer science, JSPS is pretty much the only large financial aid for Ph.D. candidates. I guess engineering and other hard sciences are more or less in the same situation. Your supervisor's grant won't support your living expenses either.
So it's quite important for most Japanese engineering/science students to be in excellent labs because in many fields you can't do research or write a paper alone; whether you can get a salary and grand from JSPS depends hugely on your lab unless you're majoring in math, theoretical physics or something along those lines.
So if you can take advantage of the Monkasho scholarship thing for international students, you definitely should. There aren't many financial aids.
Edited: 2010-06-22, 7:55 pm