After download, you need to extract the .zip (or .tgz) file, go inside the extracted folder and run the following command using PHP 5.4+:
$ php -S 0.0.0.0:8888 -t public public/index.php
You can start Apigility opening your browser to http://localhost:8888
If you are using PHP < 5.4
You need to configure a web server to publish the public folder of Apigility.
Use any port
While the above command uses port 8888, you can substitute any available port on your system.
You can also install Apigility without downloading the previous package, using the following command in your terminal (make sure your internet connection is enabled):
$ curl -sS https://apigility.org/install | php
If you do not have curl installed you can use PHP itself:
$ php -r "readfile('https://apigility.org/install');" | php