are you saying that you only have an undergraduate degree? if so, then you have to enter the masters course first.
both masters course and PhD course students must "enroll" into the graduate school.
like fustrateddave said, you cant just sign up. you have to get acceptance from a professor. But contrary to what dave said, you dont always need japanese language skills(especially in science, the japanese student are suppose to know english) and sometimes the entrance exam is just a formality. My lab has 4 doctoral students and they only know how to say konnichiha, and they just wrote their names on the entrance exam.
I believe you are talking about "stipends", not scholarships. giving stipends to graduate students is common in America too. but im not exactly sure about stipends in japan, but i know there are several students here they are receiving stipends from the lab, not the school...