Right-handed golfers wear gloves on their left hands because that is the hand that is used for the grip and vice versa. This is because when you take the aim, the opposite hand is used for the swing even though the strength is coming from the other one. But, it is totally up to you so whichever hand you feel comfortable with is the one you should be wearing your gloves on. Some experts also suggest wearing both as they look stylish and you don't have to keep removing them.