Is it possible to make the website unavailable while editing it, while online?
If so, what is the method called and how is it done?
I have a webhosting company so it's not my own server!
Typically, people use the .htaccess to password protect it until you are ready to show it to the world
Here is a link to an article with instructions
http://www.elated.com/articles/password-protecting-your-pages-with-htaccess/