A righteous Noahide is a Gentile who recognizes the divinity of the Torah and observes its prohibitions of (1) idolatry, (2) blasphemy, (3) homicide, (4) forbidden relations, (5) robbery, (6) eating meat that was taken from a still-living animal (cruelty to animals), and the requirement (7) for societies to establish courts of justice. The main and best book on details of Noahide observance is "The Divine Code" by Rabbi Moshe Weiner.