Install the plugin only if JoomGallery extension is installed on your site and you want to integrate sexy lightbox with galleries created by JoomGallery component. Otherwise the plugin doesn't make sense. The plugin is required System - ARI Sexy Lightbox plugin for the correct operation so install it first.
Install the plugin as a regular Joomla! plugin. It doesn't require any additional actions. The tutorial on how to install Joomla! extensions can be found here.