The Lord told a man named Nephi to leave so that his brothers wouldn't kill him.
The Lord was with them (Nephi and the people who went with him) and they prospered "exceedingly." They had brought records -- scriptures -- with them. They had the priesthood, they worked with their hands, they built a temple "after the manner of the temple of Solomon," and children were born. They "lived after the manner of happiness."
I really really like the last section, where Nephi wrote about the importance of writing things down. Verse 32 is my favorite:
He is such a great example of obedience!
29 And I, Nephi, had kept the records upon my plates, which I had made, of my people thus far.
30 And it came to pass that the Lord God said unto me: Make other plates; and thou shalt engraven many things upon them which are good in my sight, for the profit of thy people.31 Wherefore, I, Nephi, to be obedient to the commandments of the Lord, went and made these plates upon which I have engraven these things.
You can read the whole chapter (2 Nephi 5) from the Book of Mormon here: https://www.lds.org/scriptures/bofm/2-ne/5?lang=eng