Download and unzip the plugin. You should now have a plugin directory (Windows) or package (Mac) called 'TPG-LR-Backup.lrplugin'. If your unzip program didn't create the directory or package, then you should manually create it and copy your unzipped files into it.
The plugin is installed via the Lightroom plugin manager.
If you have donated towards the plugin you should unlock the trial version using the registration code that you should have received.