Something does not sound right here...
When you click on the 'download' link for a skin such as 'The Fly', MC should download and apply the skin automatically. If MC is not running at the time, the action of downloading a skin from the website should cause MC to launch, with it's new skin already applied.
If that's not happening for you, we should find out why...
Can you tell us:
Which browser do you use for browsing the web?
Which version of MC are you running?
What version of Windows are you running?
What actually happens when you click a download link on the skin pages?
When you click the "Download" link on the skins webpage, by default, the Media Center Package Installer should handle the download. If it does, then something is preventing it from working, possibly firewall restrictions or Windows permissions.
If the Package Installer is not handling the download automatically, and your browser is asking you to save the .mjp file instead, then you should be able to fix that in your browser configuration, though even at that, the package installer should still fire up if you double click a downloaded .mjp file.
-marko