I am reading about the zener diode, and from my understanding the zener diode adjusts its internal resistance and so the current going through it to keep the voltage across it to a specific voltage characteristic of the zener diode.

Usually, for resistors for example, the independent variable is voltage and the current is figured out by the voltage. but in the case of the zener diode it seems like it's backward.

How does it work exactly? If the state of the diode (whether current is flowing or not) is determined by the voltage applied across it then how come the it also controls its current do keep a specified voltage across it?

I'm having trouble understanding what is the independent variable and what depends on the circuit and the diode.

What happens when I apply some arbitrary voltage across it's end, say 15v, to a diode rated 5v?

 

Go to check this :
The Equivalent Circuit of Zener diode Using Diode and LED Protection.

 

The zener diode is not intended to have a voltage source applied directly across it with no resistance. What would be the point? Current would just flow across it. Normally, you'd put a resistor in series with it. Then, its great strength is that it would regulate the voltage to its rated voltage level -- within a small margin of error -- even if the overall supply voltage fluctuated. The reason its voltage _does_ vary as the current across it changes is because it's not an ideal device. There's a curve:
http://en.wikipedia.org/wiki/File:Diode-IV-Curve.svg

Normally, you'd choose a resistor such that the remaining voltage of the supply, after the zener's nominal drop, will provide a particular amount of current which is in the middle of the useful curve of the particular device. This is called the "zener test current" or Izt.

http://sound.westhost.com/appnotes/an008.htm