On the Top Menu Bar click on System->Administration->Synaptic Package Manager
Search for Skype
Click on the checkbox next to the package skype and click on MARK FOR COMPLETE REMOVAL
Click on Apply and a Summary Window will pop up. Click on Apply again.
The uninstall process should start by Removing Skype and Applying Changes. Then Skype should be removed from Computer with operating system Ubuntu.
NOTE: This has been tested on Ubuntu 9.04
Image Credits: Photo by Isis França on Unsplash.