Apart from the generic procedure that is common for most university applications when applying to a university abroad, Japan has a few particulars. You can read about the generic procedure in this yocket article which essentially elaborates well-known steps like – the English language proficiency tests, letters of recommendations, university shortlisting aid and more.
One of the specifics of applying in Japan is that one needs to prepare for are entrance exams. Japan is one of the most competitive education systems in the world and applicants have a really hard time getting through universities of their choice. Entrance exams, a common screening process, are common for both local and foreign applicants, however much harder for the locals.
Foreign students have to undertake the Examination for Japanese University Admission for International Students; abbreviated as EJU and popularly termed as the ‘Japan and the world’ exam. Most universities require applicants to take this exam to qualify for admissions, irrespective of their knowledge of the Japanese language. You can ascertain more about this exam on this link by the Japan Students Services Organization; or enquire with the local embassy in your country. A good score in this exam can also help you land a scholarship.
While this paints a rough picture, it is always advisable to check specific course requirements from your university website.