To disable directory browsing you can use a htaccess file. Open up a text editor (eg Notepad) and put the following line in it:

Options -Indexes

Now select Save As… from the menu and select ‘All files’ in the Save as type bit before typing a filename. For the filename then type ‘.htaccess’ (without quote marks and remember the dot at the start).
Next simply upload this to your public_html directory and the browsing of directories on your account will be disabled.