Out of the box, this package will send notifications as emails.
You can customize the content of the mail by publishing the views:
php artisan vendor:publish --tag="comments-views"
You'll find the Blade views to customize in resources/vendor/comments/.
To customize the notifications itself (to for instance add new channels) you create your own notification class that extends either Spatie\Comments\Notifications\PendingCommentNotification or Spatie\Comments\Notifications\ApprovedCommentNotification. You should specify your class name in the pending_comment or approved_comment key of the comments config file.