To use this script click on the "Download ZIP" button listed on the GitHub Gist page and then unpack the .zip archive locally. You should now have a directory containing the file "latest-pepper-flash.sh".
Open a terminal within that directory and run the script like so:
sh latest-pepper-flash.sh
The script will fetch and install the latest Pepper Flash. From time to time (perhaps once a month) you should re-run this script and if there is a newer Flash it will upgrade your installed copy, otherwise it will just confirm that you have the latest version.