Skype is compiled for Linux but not for arm cpu that Raspberry Pi uses, so how can I run Skype on Raspberry Pi?
Here is direct instruction how to run Skype on raspberry pi.
If you need Skype as a chat client only, a much easier way to do is it is through a Pidgin plugin that's using Skype Web internally. You can download the plugin compiled for the RPi from http://www.zhekov.org/articles/2/skype-chat-on-raspberry-pi
At the moment (this date) the only option is to install Android then use the Skype APK. Not all webcam work, but basic Skype function are available.