How should I add JavaScript to a child theme?

You can do different things:

1. Enqueue the new JS file via plugin
2. Enqueue the new JS file via functions.php
3. Add your JS code into functions.php through wp_header or wp_footer

For adding new JS files to a wordpress site you should enqueue these files with wp_enqueue_style() and/or wp_enqueue_script().

This is the proper and safest way.

I would go the route and create a simple, small plugin for that, because this is theme independent.

You could also use an hook to wp_header or wp_footer. Inside this hook you can write your JS code.

But the proper way is enqueueing these files which will work something like this:

function prfx_frontend_enqueue() {
    wp_enqueue_style( 'my-plugin-css', plugins_url('/assets/css/plugin.css', __FILE__) );
    wp_enqueue_script( 'my-plugin-js', plugins_url('/assets/js/jquery.my-script-min.js', __FILE__), array('jquery'));
}
add_action('wp_enqueue_scripts', 'prfx_frontend_enqueue');

Yes.

Add the javascript file to the folder and call wp_enqueue_script() with the proper filename. You can do this either in the child theme or a plugin, it really does not matter (from a technical perspective).

If you aren't adding more functionality, I would not create a custom plugin for this and just include it within the child theme's function.php.