1. Extract the downloaded package, you will see folders as per the opencart version. Choose the one appropriate as per your opencart version
2. You will find google-url-shortener.ocmod.zip within the folder
3. Open your admin panel and go to Extensions > Extension Installer
4. Upload google-url-shortener.ocmod.zip 
5. Go to Extensions > Modifications. Click on Refresh. You will find Google URL Shortener Library in the modification list
6. Now go to Extensions > Extensions > Modules (Extensions > Modules for opencart 2200 and older version).
7. Find Google URL Shortener and click on install button 
8. Now Click on Edit button
9. Enter the API key from your google console and save it here
10. Test the Extension

Note: OpenCart 3.x.x.x will show the message that module is disabled. This is not a module that can to be added by layout to store front. It is a plugin. Therefore It is completely fine.