First you have to enable the Canonical repository.
Open Terminal(Alt + Ctrl + T) and paste the following command to enable the repository.
You can also use this commands in Linux Mint to enable the repository and you are able to install Skype in it.
sudo add-apt-repository "deb http://archive.canonical.com/ $(lsb_release -sc) partner"
Update the repository.
sudo apt-get update
Finally after all the updates, paste the following command to install Skype.
sudo apt-get install skype && sudo apt-get -f install
You have successfully installed Skype 4.2 in your system.
Select Dash -> type "skype" on the space of search -> Click the icon of Skype to start the Skype.