In general, higher educational institutions in Japan announce their application procedures from June to August every year. Each educational institution has its own application procedures. In general, however, the documents that are required are as follows.

Undergraduates, junior colleges

Application form (provided by the university)
Personal resume
Certificate of senior high school graduation (anticipated graduation)
Senior high school transcript
Letter of recommendation from the principal or a teacher at your senior high school (or your last school)
Medical certificate (from a public health office or doctor)
Letter of guarantee from your guaranter living in Japan (optional).
Copy of alien registration certificate if the applicant is residing in Japan
Photo

Details including application method should be confirmed at the educational institutions of your choice.