How do I install this?

I am so confused about this window & linux thing. How do I install this on my website? Any files to upload to the FTP?

Phalcon is a PHP extention so you need access to the PHP installion to use it. You can build applications on your local host no problem but to push them live you need a VPS with windows or linux, a web server(etc) with PHP. Then you can run those commands you saw in the download section on that to install Phalcon. After you've install it on your VPS it will work with no more overhead than its already using on every account using that PHP installion.