There are 2 ways:
– download the quick install package – it contains Joomla files, template, demo content and is configured exactly as you see on the demo; you’ll have to replace the content with yours, change menus, settings of modules etc.
– download the template file only, install on your site and configure it as you want; in this case you’ll have to configure it based on what you have currently at the server.
To my mind it’s better to go with clean template install. In order to copy some styles/features from JA demo, install the quick package on test site or localhost and refer to it if you have questions “What kind of module is that? What module suffix is applied to module X? What is that component/plugin/module?” etc.