In western culture a engagement ring is worn on a ladies left ring finger. It used to be tradition that a engagement ring was to be of a woman's birth stone color. Today it is popular to choose a diamond for a engagement ring.
An engagment ring goes on your left hand, ring finger or finger right next to the pinky. The engagment ring also stays on the same finger once the wedding band is bought, the band just goes on with the engagment ring.