Don't use your left hand to make a double grip or touch the arm or the shoulder. Shake hands with the right hand and keep the left out of mischief. From infancy we enjoy being touched. The handshake is all we have left at work. Shake hands whenever you can.
Physical contact creates instant rapport.
Don't get caught at the finger tips. Match the grip and smile. Up and down three times. Let go last. The handshake is not meant to show people how strong you are.