How long are people genin before they take the chunin exam? Team 7 (Naruto's team) existed for at least while before they took the chunin exam, and they took on a number of missions before taking the chunin exams. I can't remember, however, how long they exactly existed as a team before the exam. How long were they genin before the exam? Is that the normal length? Is there some sort of mission requirement where they have to complete a number of missions before they can take the exam?
The exams happen twice a year. The genins that participate are chosen by their group leaders. So if the group leader is of the opinion, that they are ready at age 6, he sends the genin to the exams, if he's of the opinion that they are not ready yet, he lets them wait. There is no special requirement to take the exams (at least nothing was mentioned), it's just the group leader who decides. This can be seen in chapter 35, when Kakashi, Kurenai and Asuma suggest their team for the exams. Although Iruka protests, he can't do anything against it. That does not mean, that the genin can't decide against it, though. A ninja can't be forced by his group leader to do the exam.