The following is a note from findagrave.com, but I note some differences with other sources, including the name of Nathaniel's wife and the names of some of their children:
Nehemiah Smith arrived in Plymouth, New England before March 6, 1637/8 when he applied to become a freeman of the Mass. Bay Colony. He was one of the first religious teachers in Marshfield about 1638 where Rev. Nehemiah Smith married Ann (not Sarah in church records who was the wife of his brother, George, of New Haven), daughter of Thomas Bourne of Marshfield. He was appointed May 5, 1640 to a committee of five to view all the meadows of Green Harbor (Marshfield) which were not granted and report their measurements to the general court.
The family removed to New Haven in the Colony of New Haven. The children, Sarah, Mary, Hannah & Mercy all baptized in New Haven have been ascribed to the family of Nehemiah & Ann, but are probably the children of his brother, George Smith, and Lydia (also said to be their child) was probably their daughter-in-law, Lydia (Winchester) Smith. In 1641, a cart bridge was erected over the West River in New Haven and in 1646, Nehemiah Smith agreed to care for the town's sheep in exchange for the use of certain west-side pasture (Records of the Colony & Plantation of New Haven 1638-1649 ,Charles J. Hoadley, Hartford, Conn: Case, Tiffany & Co.1857, p. 266). The family lived in Long Island for a year or two returning to New Haven, and around 1667,the then removed to New London where he received a grant of land and again to Norwich where he became a freeman in 1669.
He was one of the original proprietors of Norwich which was bought in Jun 1659 of Indian Chief Uncas and his sons. His home lot was laid out in Nov 1659. He had the largest tract of any of the first settlers and received other grants at later times. His house was about 57 feet north of the oldest burying Ground known as Post Gager Burying Ground. He raised sheep and wove cloth from the wool. He was called "Shepherd Smith" and "Mr." Smith in respect of him being a pastor in his early years. At the county court in Norwich in 1666, "Nehemiah Smith of Norwich declaring himself above 60 yrs. of age and his brother John declaring the same at the earnest desire is freed from training."
He conveyed land to his nephew, Edward Smith on Nov. 18, 1668, and he and his wife, Ann, deeded their homestead to their son-in-law on June 12, 1684 "in consideration of maintenance for the remainder of their lives".
He died in 1686 and left a will that was subsequently destroyed along with other records.
The children of Nehemiah & Ann: Mary, wife of Samuel Raymond; Ann, wife of Thomas Bradford; Elizabeth, wife of Joshua Raymond, Experience, wife of Joshua Abel; and Nehemiah Smith, Jr.