I signed up for Skype during a flight layover in Taipei. Something went wrong. I get a screen that says "Skype cannot connect" when I clicked on "get help fixing this problem" it says "contact your network administrator". I don’tknow who my network administrator is and how do I contact him ?

If you are using your PC at home or on the road, then you are the network administrator for you PC.

What the error is really telling you is that Skype cannot find a clear path through the current network connection to the Internet.

Possibly the network router or firewall you are connection through is blocking essential ports that Skype needs to access the Internet.
At least make sure Windows Firewall is "allowing" Skype to access the Internet.

Depending on where you are trying to connect from, some ISP’s intentionally Block Skype, in which case you may be out of luck.

Confirm this by trying another VoIP client softphone like Gizmo5 or Efonica. Or try a SIP-based VoIp service like CallCentric and their free downloadable softphone.

But, again depending on where you are located, some countries may block All VoIP services that the government has sanctioned.