Hi,
The plugin offers a way to add these links via the nav menu (a Language Links box will appear in the left column of the menu editor), however there’s not much of a built-in utility for printing a language nav outside of the template, since I didn’t want to lock-in the markup (though I could write something with config options for it).
In most cases on my projects, I write something like this in the header template.
<nav class="language-nav" role="Language">
<?php foreach ( nLingual\Registry::languages() as $i => $language ) : ?>
<?php echo $i ? '/' : ''; ?>
<a rel="alternate"
href="<?= nLingual\Rewriter::localize_here( $language ) ?>"
hreflang="<?= $language->locale_name ?>"
class="<?php echo nLingual\Registry::is_language_current( $language ) ? 'is-current' : ''; ?>"
><?= $language->short_name ?></a>
<?php endforeach; ?>
</nav>
That will print a <nav> element with an >a< link for each language the site supports, flaging the current one with the is-current class. The aria-label might be tricky to implement (maybe a sprintf() call using a localized string), but otherwise that should do the job.