cd public_html would take you to your public_html directory if you were in your home directory.
cd .. will take you up one directory, so if you were in public_html it would take you to your home directory.
cd $home will take you to your home ditrectory no matter where you are.
Whenever you want to find out more about a Unix command or program enter: man command_name at the prompt. Most, but not all, will have man pages.
Probably the easiest Unix text editor to use is pico. To edit file.html, enter: pico file.html
See Also: Files, Directories & Permissions