After a bit of mucking around, I got it to work…
Using this page’s source code as a base:
https://nextgen-gallery.com/templates/example-1/
1. Download this CSS file as save it on your own sever in the wp-content/plugins/nextgen-gallery/css folder as ngg_YOUR_THEME_NAME_HERE.css.
https://nextgen-gallery.com/wp-content/themes/default/nggallery.css?ver=1.0.0
2. Download all the images that are referred to in the above CSS file and put them on your own server. For example:
https://nextgen-gallery.com/wp-content/themes/default/images/round-corner.png
3. Duplicate the gallery.php file. Rename it gallery-YOUR_THEME_NAME_HERE.php. Edit the source so that it references the CSS style you want. Check this source code for an example:
https://nextgen-gallery.com/templates/example-1/
4. Upload this file to wp-content/themes/YOUR_CURRENT_WP_THEME/nggallery
5. Use this shortcode: [nggallery id=1 template=sample1]
6. That’s it! It should work now! Good luck!