Check out system requirements on https://www.neos.io/develop/download.html You basicly need PHP 5.5, MySQL and Composer for installing dependencies.
First you need to clone the repository from GitHub.
After that go to your repository root directory and install all needed composer dependencies like this:
composer install
The site pacakge depends on minified css and js files. You can have a look into stylsheets and scripts section of default page template. The minified files are created via grunt which is configured with package.json also located in the site package. Usally you have to change into the site package directory an call grunt threre. But there is a shorthand located in the root dir. For creating minified assets call:
./publishassets.sh
To set up your websever follow instrutions on https://www.neos.io/develop/download.html. After that call http://your-neos.local/setup. and follow the on-screen instructions to set up database.