How do I implement jPanelMenu?

You can “initialize” the script any time after it has been loaded on the page. I usually do that in wp_footer (Especially if you enqueue the script in the footer) but you can add it to wp_head too.

add_action( 'wp_footer', 'wpa_107420_footer_script' );

function wpa_107420_footer_script(){ ?>

<script type="text/javascript">
    jQuery(document).ready(function($) {
        // Stuff to do as soon as the DOM is ready;
            var jPM = $.jPanelMenu({
            menu: '#custom-menu-selector',
            trigger: '.custom-menu-trigger-selector'
        });
    });
</script>

}

You’ll need to modify the script part per the instructions on the jPanelMenu plugin. That part’s off-topic here, but this is how you’d add the script to WordPress.