To customise the output of your invoices/packing notes/etc., for all formats except the “internal” (short) format, you should follow the link (from the WooCommerce -> PrintNode page, in the ‘Settings’ tab) to the settings for the plugin that creates the document, and use the options provided there. You can also create your own templates for those options (guided by the documentation for the relevant plugin). If you are using “PDF Invoicing and Packing Slips” by WP Overnight (which is our recommended partner plugin), then their documentation is available here.
To customise the “internal” format’s template, you have various options. The output is created by the file templates/cloud-print.php found in the plugin’s directory (wp-content/plugins/woocommerce-printorders). You can copy this file as templates/cloud-print.php in your theme or child theme directory, and then modify it. Instructions are at the top of that file. If you simply wish to add or change CSS styles, then this can also be done with a hook (the woocommerce_printorders_css filter). Alternatively, you can use the woocommerce_printorders_printtemplate filter to use a template of your own devising at a different location. There are various other hooks that may be better than copying the template, for simple tasks.
For customising other aspects of its behaviour, this plugin uses WordPress’s standard customisation mechanisms – hooks and filters. As with every other such plugin, a competent developer can read the plugin code, and hook into it at any of those points (see here, or here for a tutorial). (Please note that customised development is not included in the purchase price of any plugins).
Finally, you may find the debugging log feature useful – this is configured in WooCommerce -> PrintNode -> Settings. WooCommerce’s standard logging mechanism is also used, so you can also find logs in your WooCommerce log directory (usually wp-content/uploads/wc-logs).