Open the Applications Menu (the third icon down on the left, below the "two people" Contacts icon). Skype should be the fifth application listed (counting from the top). If you haven't installed Skype, then clicking the Skype icon will begin the installation process. Once installed, the same icon starts Skype.

I don't think you should have done what you have done - which is to install manually via the App Manager. When installing via the Skype icon, you end up with all of the locals (including those you don't need - sigh) so you may now have a partial insall. See if you can uninstall what you have so far installed, then install via the Skype icon.