So if you have ever logged into a WordPress admin and viewed the site while logged in I am sure you have seen the Edit this link at some point. Some themes have them and some do not though.
To remove this open up your Appearance>Editor and then select a page.php or index.php to locate this code. Generally you can find it in your page.php, single.php or index.php.
<?php edit_post_link(__('Edit This')); ?>
To add this link into your site just open the correct WordPress template file you want it to show and add that line of code. You can change the ‘Edit This’ text to anything you wish.
You will only see when logged into the site so you don’t have to worry about viewers seeing it.