Shaking hands is a relic from the past. When primitive tribes met under friendly conditions, they would hold their arms out with their palms exposed to show no weapon was being concealed.
In Roman times, the practice of carrying a concealed dagger in the sleeve was common and so for protection the Romans developed the ‘lower arm grasp’ as a common greeting.
The modern form of this is the interlocking of the palms and was originally used in the 19th century to seal commercial deals between men of equal status.
Today it is the expected greeting between two business people (be culturally aware here as in some cultures there are different guidelines).
To do it well, stand square on to the other person, extend your arm from the shoulder bending it at the elbow, interlock web to web (this is the skin between your thumb and forefinger), make eye contact and smile. Give 3-4 up and down shakes and say it’s good to meet them.