Túrin ruled Gondor during the time known as the Watchful Peace, during which Sauron had withdrawn into the east and did not trouble the western lands of Middle-earth. Hence, his time as Steward was rather uneventful in historical terms, except perhaps for the highly unusual circumstance that he married twice.
Túrin ruled as Steward for thirty-four years, and was succeeded by his son Hador.
The date of Túrin's birth appears only in The History of Middle-earth volume XII, The Peoples of Middle-earth. It cannot therefore be considered completely reliable. The same source offers some interesting insights into Túrin's biography. He was apparently married twice, and had many children, though his only son Hador was born near the end of his life.