Proper form of greeting?

What or how is the proper way to greet a Muslim,...besides a handshake. And how does a man greet a woman for conversation, I mean that in a strictly non elationship way, like if my wife and i are together and I where to great her for a reason like business and or somethng else, do you extend your hand to shake hands? Or is that forbidden. I have seen some, cup their hand and make a gesture like putting their hand in front of their mouth, and kind of waving?(no they werent yawning)? Not sure if that is related....or if i described that right. I do know that you are to use your right hand only because the left is used for...clean up.

Thanks and God be with you.

Hi there!

If a Muslim man greets a Muslim woman then "assalamu alaikum" would be the way but if it's a non-mahram it should be done in a polite but not in too friendly way.

If a non-Muslim greets a Muslim of the same gender then just "Hello" or some other usual greeting word would be okay and can be accompanied with a handshake. It's the same with a Muslim greeting a non-Muslim of the same gender: a handshake if liked so and an usual greeting such as "Hello" or "Good morning" is better to use as the non-Muslim may not know what "assalamu alaikum" means and may not understand the bigger meaning behind it.

But if it's a non-Muslim man greeting a Muslim woman then "Hello" would go as well but it's definitely better not to extend your hand as in Islam we are to avoid handshakes with the opposite gender. But we also are not ordered by islam to reject the handshake when we find ourselves in such a situation where a person from the opposite gender extends a hand to greet us.