Is it possible to get a list of files under a directory of a website? How?

Yes, you can, but you need a few tools first. You need to know a little about basic coding, FTP clients, port scanners and brute force tools, if it has a .htaccess file.

If not just try tgp.linkurl.htm or html, ie default.html, www/home/siteurl/web/, or wap /index/ default /includes/ main/ files/ images/ pics/ vids/, could be possible file locations on the server, so try all of them so www/home/siteurl/web/includes/.htaccess or default.html. You'll hit a file after a few tries then work off that. Yahoo has a site file viewer too: you can try to scan sites file indexes.

Alternatively, try brutus aet, trin00, trinity.x, or whiteshark airtool to crack the site's FTP login (but it's illegal and I do not condone that).

DirBuster is such a hacking script that guesses a bunch of common names as nsanders had mentioned. It literally brute forces lists of common words and file endings (.html, .php) and over time figures out the directory structure of such sites, this could discover the page as you described but would also discover many others.

If you have directory listing disabled in your webserver, then the only way somebody will find it is by guessing or by finding a link to it.

That said, I've seen hacking scripts attempt to "guess" a whole bunch of these common names. secret.html would probably be in such a guess list.

The more reasonable solution is to restrict access using a username/password via a htaccess file (for apache) or the equivalent setting for whatever webserver you're using.

There are only two ways to find a web page: through a link or by listing the directory.

Usually, web servers disable directory listing, so if there is really no link to the page, then it cannot be found.

BUT: information about the page may get out in ways you don't expect. For example, if a user with Google Toolbar visits your page, then Google may know about the page, and it can appear in its index. That will be a link to your page.