Goku, a saijin, was born on planet vegeta and sent to earth as a child to destroy it. When there he bumped his head on a rock and became good and was then trained by his master Gohan (his grandfather not his son) and Master Roshi. He then met Kurlin and met many obstacles in the Dragonball series which prepared him for Dragonball Z and GT. Goku is the strongest warrior throughout most of the series.
Gohan
Gohan is Goku's First son who was born on earth, that is half saiyan and half human. Gohan discovers his powers in the Saiyan Saga or Vegeta Saga and learns to control them w/ the help of Piccolo, who trained him when Goku was dead. Later in the series Gohan gets his power awakened by Guru and becomes much stronger and helps in the fight against Freiza. Gohan later becomes as strong as Goku and becomes the second strongest fighter.
Goten
Goten is Goku's second son who is very powerful for his age. Goten looks almost the same as Goku as a child. Goten can fuse with trunks to form gotenks who is really powerful.
Trunks
Trunks is Vegita's and Bulma's son who is half sayain and half human. Trunks comes from the future in the cell saga and destroys Frieza and King Cold for the last time while Goku was still off the planet. He also is born after the Z series and has the power to fuse with his best friend Goten
Veggita
Veggita is the prince of the former Planet Veggita where he was born and raised until destroyed by Frieza. Veggita is introduced in the Veggita Knappa Saga where he attacks Earth in search of the DBalls. he is then met by Goku and is defeated in battle and retreats. He later becomes good and has a son named trunks with Bulma.