You won't be able to put skype on an arduino.
Skype is inherintly OS based, as PaulS said, and the arduino doesn't really have an OS.
That said, it might be possible to make something like skype.
You would need a microphone and some method of playing sound.
How feasible this would be, I don't know, I'm geussing it would be severely stretching the abilities of the arduino if you can make it work.
If you're going to try, good luck 