Bheng
Your web site trys to open a file called index.html (or index.htm) when you use your browser to go to it online.
For example, entering
http://www.websitebabble.com/ would open a file at that location called index.html. [ok, don't try it because Lisa uses php programming and you have to use index.php to get it to work, but let's not complicate the issue!]
If this is what you are trying (yourdomain.com) and not getting your page there are two possibilities. One is that you did not load a page with that exact name or second, you put it into the wrong folder on your host.
Getting it into the right folder is a little difficult for some people. The index.html file must be in your root folder. That should be the one that is labeled like your domain name.
Open up your site with FileZilla (you can connect just as if you were going to upload another file) and look at the file index.html to see that it is correctly named and placed in the right folder. It is hard to imagine that your problem is anything else since the file works on your computer. Since you said you have it on your computer, if you don't find it on your domain you just upload it to the correct folder with FileZilla--drag and drop it is the easy way.
As far as editing, just edit your files on your computer as you have done, then upload and overwrite files on the site to update them.