During this age of Jesus, the bible was very silent about this. Maybe because of the limited sources about the life of Jesus. When we are asked about the life of Jesus when he was between 12 to 30 years old maybe we can say "WE DON'T KNOW!!!".
But a lack of information in scripture has never stopped scholars from theorizing, especially when there is internal evidence, that is, evidence we can deduce from the literature itself, to support a pet theory. So, here are three theories I have encountered in my studies.
The first theory is considered by most of the Orthodox Christian. It was been said that Jesus remained in his father's home and learned the family business. This was the most common path that the Jewish people will follow or we can say that this was part of their culture.
The second theory suggests that Jesus joined Essenes in the Dead Sea area to become a monk or separatist. Essenes are those who believed that they were holy and so they will be separated from being unholy. They left Jerusalem and civilization to study the scripture and live the separatist life in wilderness. It was also said that, maybe Jesus and John the Baptist adopted the rites of baptism.
The third theory is that Jesus went to India or some parts of Near East to study Buddhism. We can say that this was happened because of the parallel teaching of Jesus and the Buddhism in which they believed of life after death and oneness of God.
Scholars says, "His education would have been severly limited if he remained in Nazareth. Surely he got his education from somewhere else; and it must have been somewhere radical, because of his radical interpretation of scripture.
So here are three current theories as to what Jesus did during that 18 years or so between his temple visit as a child and the beginning of his public ministry. Which one is the historical reality? We will likely never know because it wasn't deemed important enough to record by those who knew Jesus best. Perhaps we too must be satisfied with this.