Upload the whole plugin folder to your /wp-content/plugins/ folder.
Give the folders in the Plugin dir write permission (777) => wp-mpdf/cache AND wp-mpdf/graph_cache
Go to the Plugins page and activate the plugin.
Add to your template "<?php if(function_exists('mpdf_pdfbutton')) mpdf_pdfbutton(); ?>" for a small button or "<?php if(function_exists('mpdf_pdfbutton')) mpdf_pdfbutton('my link'); ?>" for a textlink.
(if you wish to open the pdf print in a new tab you can add as first parameter true)
You can adjust some options if you go to your admin interface, klick on plugins and then on wp-mpdf. For pdf allow you can use the checkbox when you create or edit a Post or Site.