There are mostly two intakes, April and October for most Japanese school in Japan. Some schools often have start dates in January and July as well, but they don’t offer the cheap courses.
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. If you want to study in Senmon Gakko or Technical course in Japan you will usually need to take an exam to show that you can fulfill their requirements. The fee is higher as compared to language study in Japan through a Senmon Gakko and it usually demands N2 with particular experience in the pertinent field you are going to apply in. Fees can be paid fully or partly. In case of part payment, rest of the installments can be given after reaching Japan and getting Job, 3 months after reaching Japan in most of the cases. For application, as mentioned earlier, the procedure starts from Documents verification, Form writing, Translations, Essay writing in both the languages, Guarantor verification, Bank statement verification, POS approval, ID Number generation, COE issuance, Visa application and Tickets confirmation. If all goes well, usually COE is issued prior to one month of scheduled intake and after that Visa application and fees submission takes place. Application process can be long and tedious in some cases where the financial guarantor is not directly related to the applicant and there are various local immigration regulations depending on the school location in Japan the applicant is applying in. The guarantor also can be a local resident of Japan if directly related to the applicant and he has to declare all is necessary documents to the local immigration in Japan showing his capability to sponsor the applicant in case needed. Also check Nihongomax videos about this topic on YouTube.