Log into your SkyPrivate account. Once this is done, click on "Download Skype Plugin".
Select the version that you need, the one for Windows or the one for Mac.
The plugin will start downloading. After the download is complete, click on it.
A pop-up will appear where you should click "Install".
Before the plugin is installed, Skype and the plugin will ask you to Allow or Deny the plugin's access to Skype. Click on "Allow access". This will happen if you are logged in Skype. If you are not logged in, you will need to login.
After doing so, the final step will be to log into the plugin.
If your Skyprivate Username matches your Skype one, everything will be fine and you will appear as logged in.
Attention! check both your Skype and Skyprivate username. They need to match in order to appear as logged in.