Each year, beginning in September or October, many Japanese consulates around the world open up applications for the JET Programme which close late November or early December. The dates change each year, so make sure you check with your consulate when you need to have your application in by. If your application is successful, you will be asked back for an interview. After this stage you may be rejected, put on an alternate list, or the shortlist. Shortlisted applicants usually receive notification of a placement somewhere in Japan shortly afterward. You will either depart in April or late July/early August, depending on the preference you listed on your application and the availability of positions. Alternates may or may not receive a placement after this time for up to several months, sometimes even after regular departure.
The whole process can take 9-10 months between initial application and arrival in Japan.
There are two main types of jobs:
ALT: Assistant Language Teachers at schools and Boards of Education. Primary responsibility is usually to assist teaching English to pupils at Elementary/Primary School, Junior High School, and Senior High School levels. Some Prefectures employ non-English speaking ALTs to teach other languages.
CIR: Coordinator of International Relations at government or municipal offices, international organizations, and others. Primary responsibilities can include translating, interpreting, planning events, and more.
Although this typically, but not exclusively, applies to CIRs, your position may also include the responsibilities of a Prefectural Advisor from Day 1. You cannot apply directly for this position when applying for JET.
There are also SEAs, who are Sports Exchange Advisors, but you cannot apply for these positions and they are very uncommon.