DragonBall Z starts 10 years later from the original Dragon Ball series Goku has a child Gohan names after Goku's Grandfather and Goku has been told that more Saiyans are coming to earth and that Goku needs to train hard for their arrival. Gokus brother Raditz shows up and come to find out that he is too much for Goku and his son Gohan even with the help of a long time rival Piccolo who feels the earth is hi and that's why he helps Goku.

This is how DragonBallz starts out and there are anymore series in the Dragon Ball Z realm.