I'd say there are a couple of approaches for this, but I'll just show you the easiest.
Before anything, the most important step is, take a backup of your site, either manually or using Akeeba Backup.
Now, in the quickstart zip file, it should show the entire Joomla site.
From this zip file, extract the following directories on to your computer:
Once done, zip all these directories up, and upload the zip file to the root of you online Joomla site. The extract it.
Login to the Joomla administrator and go to:
Extensions (top menu) >> Manage >> Discover
It should show you a list of all the extensions from the quickstart package (including the template) and allow you to install them.
Hope this helps