The Japanese school year starts in April and the second semester usually starts in October. Language schools often have start dates in January and July as well, and short term courses start every month at some schools.
For long term courses on student visa you need to apply approximately 6 months in advance to most language schools due to the visa application that is done through the school. Universities and high ranking schools can handle the visa process quicker but they often set their deadlines about 6 months before the course starts anyway. Some universities only take applications during a couple of short application windows so make sure to check the application information of the university that you are interested in.
If students want to study Schools or University in Japan they will usually need to take an exam to show that they can fulfill their requirements. Japanese schools usually demands JLPT 2 while universities favor the EJU-exam.