How do you shake someone's hand

This is depending on culture of the people, but in the western ways offering a handshake is good way to say that the person is very much appreciated and welcome or you both are agreeing to a certain thing, and are very happy that you have spoken to each other about it. I think another way to handshake is to place your hand in your chest, well it is not really a handshake but a similar expression.

Normally I give people a firm handshake to show that I am not scared. If there is someone who I do not really like, I just give the person a quick handshake and let go almost immediately.

It depends on the person. but any hand shake should have a firm grip and look the person in the eyes.

If you ask me I would try shaking peoples left hand. Most people are rightys, therefore wipe their butts with that hand.

I am a very small female (95lbs 5'1"), but my father is an ex-marine. That man has the firmest handshake I have ever seen in my life, but even if a handshake is a bit too firm or uncomfortable, I find that to be a sign of personality. Typically the bigger and more open a personality someone has, the firmer their handshake is. I have often gotten surprised looks and numerous comments because I have a strong handshake for a female, let alone a small one. A firm (but not crushing) handshake is always the best route, and good eye contact shows you are an open personality and not trying to hide anything. To me, I don't like the open hand over the shake, it seems like they want you to trust them too soon and is almost claustrophobic for someone my size and can even be a bit intimidating. It all depends on the person I think. Good question though!