In 1835, Joseph Smith told a visitor that “I obtained them [the plates], and translated them into the english language; by the gift and power of God.”
English was Joseph's native language. He likely knew no other languages at the time. When we read the text, we notice it sounds a lot like the King James Bible, but it is also different. There are a lot of nonbiblical terms and phrases that Joseph used. He had to have learned these growing up.
The study of the connections between the Book of Mormon and other sources is called "intertextuality." See the page on intertextuality.
After he obtained the plates in September 1827, he moved to Harmony, Pennsylvania.
"By this timely aid was I enabled to reach the place of my destination in Pennsylvania; and immediately after my arrival there I commenced copying the characters off the plates. I copied a considerable number of them, and by means of the Urim and Thummim I translated some of them, which I did between the time I arrived at the house of my wife’s father, in the month of December, and the February following."
(Joseph Smith—History 1:62)