If you want to install Skype to an Android device, select the Google Play app and then search for Skype there. The Google Play store has the appropriate Android version of Skype.
As you can see from the screenshot below, there are 3 versions of Skype in the Google Play store. I have installed the full non-business version to my phone. My work never used Lync and doesn't use Skype so I don't need that version, and I don't want to use the lite version since it is under development.