Elgg themes are just like the other kinds of Elgg plugins you can download from here. Installing Elgg and adding plugins can be done by two ways: either by composer (command line method that requires some experience - I won't explain it any further here) or by downloading a zip file of Elgg (and for every plugin) here from the community site.

If you used a script to install Elgg, you have already got a working Elgg installation. Though I might say that in the long run you might try to get familiar to install/upgrade Elgg on your own because then you have better control about what happens. The script (Softaculous) is NOT officially supported by Elgg. It might work or not. And it might break you site in the future if the people maintaining the script don't fully support possible future updates of Elgg.

Adding a plugin (when having it as zip file) is easy. You just need to extract it into the mod folder of your installation. You should also see all the other plugin folders there that are already part of Elgg core and you would extract the new plugin that its folder is there in the same way (just make sure that you don't extract the plugin zip content into a subfolder within the plugin subfolder in mod or Elgg won't be able to use the plugin). Once you've extracted the plugin in the mod folder or copied the plugin folder into the mod folder, go to the admin area of your Elgg site and to the Plugins section there. The new plugin should appear at the bottom of the plugin list. Activate the plugin and you are done.

When adding new plugins you need to be sure that the plugin is compatible with the Elgg version you use. If the plugin says for example it's recommended for some 1.x or 2.x version of Elgg it's very, very unlikely that it will work on some version of Elgg 3. The same with the upcoming Elgg 4: if a plugin author does not recommend a plugin version for Elgg 4 it might not work (or not without problems).

When updating to a newer version of a plugin (with the zip archive of a plugin) I recommend to do it like this: 1. backup (install folder, data directory and database), 2. deactivate the plugin you want to update, 3. remove the plugin folder of this plugin in the mod directory and only then extract/copy the new version into the mod folder, 4. activate the plugin again.