Step 1. You will want to understand WordPress' do_shortcode function
Step 2. You will need to edit your template files and insert:
<?php echo do_shortcode('[print-me title="Print this page" target="body"]'); ?>
Since you are targeting the body, and it's the same on every page, you could also set up body as your default target in the plugins option page.
Since you are targeting the body and want this to be visible on every page, you could place this in your header/footer... but this really depends on WHERE you want the print icon to be displayed.
If you need further assistance, you might want to first get comfortable with making changes to your theme template files.