This is normally done on the server using special rules to rewrite the URL. If your server is Apache, and your hosting company allows you to use .htaccess with mod_rewrite, you can do it yourself, but it requires knowledge of the rather complex mod_rewrite rules.
Another way to do it is to create a folder for each file, and name the file index.html or default.html, depending on the default name used by your web server. So, a file called index.html in the about folder could be accessed as http://www.example.com/about/. However, that's a very clumsy way of doing it. You end up with a lot of folders, and all your files called index.html, which is very confusing to maintain.