The following config will discuss an installation of Skype on Ubuntu 16.04 Xenial Xerus 64-bit Linux.

Install from Ubuntu Partner Repository

Below commands will install Skype from Ubuntu's partner repository:

$ sudo add-apt-repository "deb http://archive.canonical.com/ $(lsb_release -sc) partner"
$ sudo dpkg --add-architecture i386
$ sudo apt-get update
$ sudo apt-get install skype

Skype should now be installed on you Ubuntu 16.04 system. Use Ubuntu's application menu to start Skype or start Skype directly from your terminal:

$ skype

Manual install

Start manual Skype installation by downloading the latest official skype ubuntu package from http://www.skype.com/en/download-skype/skype-for-linux website.

Alternatively use the wget command below to download Skype Ubuntu package directly from command line. Please not current version of skype may be different:

$ wget http://download.skype.com/linux/skype-ubuntu-precise_4.3.0.37-1_i386.deb

Since we are trying to perform an installation of i386 package on 64-bit system we need to enable multi-architecture to support both platforms:

$ sudo dpkg --add-architecture i386
$ sudo apt-get update

At this stage we use dpkg command to install the previously downloaded Skype package:

$ sudo dpkg -i skype-ubuntu-precise_4.3.0.37-1_i386.deb
.....
Unpacking skype:i386 (4.3.0.37-1) ...
dpkg: dependency problems prevent configuration of skype:i386:
 skype:i386 depends on libc6 (>= 2.3.6-6~).
 skype:i386 depends on libc6 (>= 2.7).
 skype:i386 depends on libgcc1 (>= 1:4.1.1).
 skype:i386 depends on libqt4-dbus (>= 4:4.5.3).
 skype:i386 depends on libqt4-network (>= 4:4.8.0).
 skype:i386 depends on libqt4-xml (>= 4:4.5.3).
 skype:i386 depends on libqtcore4 (>= 4:4.7.0~beta1).
 skype:i386 depends on libqtgui4 (>= 4:4.8.0).
 skype:i386 depends on libqtwebkit4 (>= 2.2~2011week36).
 skype:i386 depends on libstdc++6 (>= 4.2.1).
 skype:i386 depends on libx11-6.
 skype:i386 depends on libxext6.
 skype:i386 depends on libxss1.
 skype:i386 depends on libxv1.
 skype:i386 depends on libssl1.0.0.
 skype:i386 depends on libpulse0.
 skype:i386 depends on libasound2-plugins.

dpkg: error processing package skype:i386 (--install):
 dependency problems - leaving unconfigured
Processing triggers for hicolor-icon-theme (0.15-0ubuntu1) ...
Processing triggers for gnome-menus (3.13.3-6ubuntu2) ...
Processing triggers for desktop-file-utils (0.22-1ubuntu3) ...
Processing triggers for bamfdaemon (0.5.2~bzr0+16.04.20151217-0ubuntu1) ...
Rebuilding /usr/share/applications/bamf-2.index...
Processing triggers for mime-support (3.59ubuntu1) ...
Processing triggers for dbus (1.10.6-1ubuntu1) ...
Errors were encountered while processing:
 skype:i386

To fix the above dependencies problems run the bellow command which will install all required dependencies as well us the actual skype package:

# apt-get -f install
....
Setting up skype:i386 (4.3.0.37-1) ...
Setting up qt-at-spi:i386 (0.4.0-3) ...
....

Skype is now installed and ready to use. If you cannot find skype shortcut on any of the GUI menus re-login or simply start skype from terminal by typing skype command:

$ skype