To install Skype, you need to download the latest version from the Skype website. Do not download Skype from anywhere else.
The Skype install file is about 1MB in size. When you run the install file, the installer will download the Skype application (about 20MB) in the background. If your internet connection drops while this is happening, the installer will resume the download as soon as connectivity is restored.
If you do not wish to use the light installer, download the full installer (around 24MB).