In most cases the engagement ring is worn on the left hand, on the pregnant finger (right next to your pinkie). In some religious cases this may be changed. In same sex marriages, they sometimes wear...
My husband wears his on his left hand ring finger. He wears the wedding band first, closest to the palm, and the engagement ring on top of that. Hope that helps.
Men typically don't wear engagement rings. Women wear engagement and wedding rings/bands on their left hand, and men wear wedding bands on their left hand, so I assume that if a man has an engagement...