While it is not possible to access the full Skype API from a Web page, there are supported URIs in Skype that allow you to send a command to Skype from a Web page. Scenarios that it allows are:
- Call a number
- Call a Skypename
- Start a chat with a skypename or a multi-chat with multiple skypenames
- Add a skypename to contacts
- View a profile
More info here:
http://www.skype.com/share/buttons/advanced.html
You can also display your online status using a setting in Skype's privacy preferences panel.
http://www.skype.com/share/buttons/status.html