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I am not sure which PDF you've read. We removed the Joomla! update feature four years ago when we donated it to Joomla! itself (it's the Joomla! Update component you get with Joomla! itself). For a while we had a different product, Akeeba CMS Update, which duplicated that functionality. We discontinued that in March since we contributed all of the remaining features back to Joomla! itself. In fact, the reinstall / manual Joomla! update feature was contributed to Joomla! Update by yours truly and was included in Joomla! 3.6. We'll use that instead.

But first, about what your claim as far as the documentation goes. The PDF documentation of the current version at the time of your purchase, our on-line documentation (bboth built from the same source) and our product description do not lay claim to such a feature. Apparently you read some documentation from 2012 or thereabouts?

So, answering your question, the update button is in Joomla! itself. Log in to the back-end of your site and click on Components, Joomla! Update. Now click on the Upload & Update tab.

In a new tab go to https://www.joomla.org/download.html and download the Joomla! 3.6 upgrade package in ZIP format (direct link for Joomla! 3.6.0).

Go back to the Joomla Update tab in your browser. Click on the button to Choose file / Browse (depending on the browser) and locate the ZIP file you downloaded in the previous step. Click on Upload & Install. You will be asked to re-enter your username and password (it's a security feature to prevent abuse) and then Joomla! will replace its files with those in the update package.