Warning: Wikipedia contains spoilers.
Nog was born to Rom and Prinadora on Ferenginar on 2353. Later he moved with his father to Deep Space Nine and worked at his uncle Quark's bar. With Jake Sisko, he was one of the first students in Keiko O'Brien's school. Rom's imcompetence with money and proficiency with mechanics and electronics are traits he passed on to Nog. In 2371 he went through the Ferengi coming of age rite and purchased an apprenticeship with Captain Benjamin Sisko, and went on to Starfleet Academy, to become the first Ferengi in Starfleet. He participated in the Dominion War, losing his left leg in the Battle of Ar-558. Doctor Julian Bashir replaced it with a bionic leg, and Nog chose Vic Fontaine's club in the holodeck as the place to rest during recovery. Captain Sisko recognized Nog's heroism in battle.