Shaking hands dates back to medieval times. When two men met they extended their open palms towards each other to show that they were not concealing weapons in their hands. The handshake has developed from this practice.
Although it is an acquired trait, the way you shake hands could indicate your natural temperament, or the way you feel at a point in time. Placing your own hand on top by turning the other person's palm upside down indicates extreme assertiveness. Holding back even as you start to extend your hand towards a person conveys feelings of suspicion, or an unwillingness to associate with the person. Gripping too hard and grinding people's knuckles is a sure sign of aggression. If you tend towards it, do not be surprised if you're soon deserted. But the worst turn-off is what behaviourists call the 'cold fish' grip. This refers to the cold, lifeless hand-shake which denotes a total lack of conviction or genuine feeling.
The correct way to shake hands is to extend your own palm and to exert a firm grip. It implies that you've accepted the other person on equal terms and have no hang-ups about the relationship.