After making Android users wait, for what felt like an eternity, Skype has finally released an official client for Android handsets. Download it from here.
Do keep in mind that VOIP calling over 3G data connection is still not supported in the US. And for those who can't seem to find out, how to exit the application, just sign out from 'my info' tab. It'll automatically shut down the application.
Skype on Nexus One.