I know one part of the process was to first be accepted by another Rabbi as a mentor, under which the "apprentice" would then train. This was often done at an early age and a family would commit the son to this process.
Part of the training required a thorogh and complete understanding and memorization of the TORAH and I am not sure if that extended to the other books of the TaNaKh or not.
I have an article which goes into some of the detail about these earlier texts of scripture if you are curious:
There is not a lot of info about Jesus growing up as a boy unfortunately (that I am aware of--except in some of the Apocrypha or Gnostic texts) that could confirm if He participated in this type of training. I would imagine His knowledge of scripture and so forth would have been more divinely received and driven.
Many referred to Jesus as "Rabbi" out of respect for His ministry and His obviously being qualified, whether or not He had actually received this type of training or indoctrination.
That is best I can answer, being a follower of Jesus Christ and a Christian in my own background. Perhaps our more learned Jewish brothers and sisters have a better insight into this.