If you wish to obtain a new rank then you must reach all the qualifications to become that rank. All the qualifications are explained below for each rank.
Academy Student- The Only Requirement is that you have an approved character and then you will be automatically placed into this rank.
Genin- You must have been taught and know all of the academy jutsus. Also you must pass the Academy Graduation Test. Once you have done that then you are a Genin and you will be moved into this Rank. After you have been moved into this rank you will be given Two other genin members to become a Three man cell under the command of an npc Jounin, at least for now since we have no jounin.
Chuunin- You must be a genin Ranked ninja and pass the Chuunin Exams. However you must also have completed 20 missions of any rank.
Jounin/Special Jounin- You must be a Chuunin Ranked ninja and have completed 5B-Rank missions, and at least 35 lower ranked mission. If that has been completed and if your kage believes you are ready then they will approach you to become a Jounin Or special Jounin based on your skill set.
Hunter Ninja- You must be a Jounin/Special Jounin Ranked ninja and have completed 2S-Ranked missions, 10A-Ranked missions, 18 B-Ranked missions, and at least 30 lower ranked missions.
Anbu- You must be a Jounin/Special Jounin Ranked ninja and have completed 2S-Ranked missions, 10A-Ranked missions, 18 B-Ranked missions, and at least 30 lower ranked missions.
S-Ranked Ninja- You must be at least a Jounin/ Special Jounin Ranked Ninja and have completed 8S-Ranked missions, 20A-Ranked missions, 22 B-Ranked missions, and at least 30 lower ranked missions.