can anyone please explain me how to use this "ki" ?

This link may help you understand a bit more. 

http://www.turkishlanguage.co.uk/ki.htm

thank u so much it was very helpful!

Also this useful tip from si++

I think the easiest way to remember (at least for me) is to think of -ki as "that is/are" or "which is/are", so in this example you´d translate  "üstündeki kýz" - the girl that is on top ..

What the addition of -ki to any noun that ends in -de/-da is it makes it an adjective, which you´d use to describe another noun, for example: 

çevremizdeki eþyalar - things that are in our surroundings

dünyadaki en yakýþýklý Türk - the most handsome Turk that is in the world

 oh thank you Henry. the explanation with colors made it not only very clear but remembrable.

Happy to help find the information, but si++ did all the good work in colouring the explanation.

 well thanks to all who make an intresting and important knowledge seems easy and remembrable

what about this then:

hayatýmda nefesim

why cant i say hayatýmdaki nefesim?

What does "ki" mean in tabii ki?  I was told this means "Of course." Is tabii ki written correctly and what is the literal translation?

Yes it means of course.

I call it elliptical-ki (Not that a term I heard/read somewhere, I just call it so)

We had a discussion about with CynicMystic about it in this thread.

Literally

Tabii ki = it is natural that ...

Ellipses (...) usually refer to what is being talked about.

What you are saying is naturally (or of course) right.