Download the zip from: https://github.com/dwmkerr/spaceinvaders. Click Code, Download. Unzip it on your harddrive.
Get login-information to a ftp-server from your school and upload the files there, using e.g. Filezilla.
In a browser, enter the [url to the ftp-server]/spaceinvader/index.html
Read file js/spaceinvaders.js and see how input from keyboard is handled and control the starship in the coordinate system of the screen.
Take a backup copy of the file.
Comment out some things and edit some small things. Save, upload and see your own first changes to your new unique games.
When you are happy, celebrate and send the url to your friends!
Share images and screenshots in the comments below.