zOOm 1.5 is easily installed as any Joomla component. That should be done through your site's backend. Please make sure you have 

Navigate to the Joomla administrator login page and enter to your backend with an Super Administrator user.

Once you log in, you should open the Extensions -> Install/Uninstall section and click on the [Browse..] button in the Upload Package File section. Navigate to the same zOOm 1.5 file you have downloaded earlier and select it. Then click on the [Upload File & Install] button to start the installation.

At the end you will see a notification that the component integration was successfully completed. Read carefully all the messages to make sure there were no error during the installation.

At this point. zOOm 1.5 is installed and ready to use with the default settings.