Nephi had just a regular life in Jerusalem, 600 BC. He was a young man who was still learning and was taught Egyptian and Hebrew. Egypt was a major power at the time and Nephi needed to learn the knowledge he needed to be successful. The Jews hoped the Egyptians would support them against the growing power of Babylon. It is similar to how many Americans want their children to learn Chinese for they feel like China is the future for America's success. Just like the Jews of old, Americans are probably wrong in that assessment. Anyways, Nephi learning Egyptian ended up being useful for he was able to write more on the plates in a smaller amount of space. Now, that Nephi was older, it was all about Babylon! Jerusalem was under their thumb but believed that by paying tribute they would be saved. They now had a new young king, Zedekiah, a puppet of the Babylonian king.
Nephi, had a normal life in Jerusalem, perhaps his family was mocked for being what they would call "fundies" today. People who actually follow their religion! Lehi's family followed the Law of Moses beyond just tradition and culture. They believed in it. Laman and Lemuel, Lehi's older sons, loved their father, but thought he was out of touch. There is a new world out there! Behold the great Egypt and Babylon! That is the future!
Then everything changed. Lehi went out and prayed and received a revelation. I can imagine how this memory remained fresh in Nephi's mind years later when he wrote the account in The Book of Nephi. Imagine, your day is going on like normal and you see your father stumbling home exhausted and rushing to bed. Was he sick? What was going on? After his father told him about what the Lord revealed to him Nephi knew that was the moment everything changed in their life. That is when his father received his calling to warn Jerusalem of its destruction. Remember "Surely the Lord will do nothing, but he revealeth his secret unto his servants the prophets." (Amos 3:7)
Lehi saw not only the destruction of Jerusalem, but he saw God and the Lord Jesus Christ. (he saw ONE descending, usually ONE is Jesus Christ) I can't imagine what I would think if I saw my father after such an experience. This memory made a lasting impression on Nephi who included into his own record.
The time when Lehi began his ministry was also a time of trials for the family of Nephi. They were rejected and mocked, Lehi even had his life threatened. Even through all of this Nephi saw "the tender mercies of the Lord". The rest of the 1st Book of Nephi relates this point. It is the exodus of Lehi's family and all they endured in order to start a new nation under God.