"SkypeKit is no longer accepting new developer registrations. If you are developing websites or applications that you want to integrate with Skype, check out the Skype URIs."

and

How Skype URIs work

In its simplest form, you can embed a hyperlink referencing a Skype URI in a webpage to place a Skype call. For example, to initiate a call to the Skype Echo / Sound Test Service, the link would be:
<a href="skype:echo123?call">Call the Skype Echo / Sound Test Service</a>Clicking the link:

1. Brings the device’s Skype client into focus, starting it as necessary.
2. Effects auto-login or prompts your users for their Skype Name and password.
3. Typically opens a confirmation dialog to authorize placing the call.
4. Places the call