Just go to the main page of your site and, if you're using Firefox, right click and select "View page source" (IE & Safari can do the same I just can't remember what their particular commands are).
Then, do a search on the code (cntrl-f) for "favicon.ico". Sometimes the favicon.ico is in the template, sometimes it's in the default joomla installation. That should give you the path to the ico file. For some reason the favicon on my own site is:
<link rel="shortcut icon" href="/images/favicon.ico" />
which means it's in the main images directory in that particular case.
Then, once you've got the path, just replace the ico file with your own (using an FTP program).
If your site is "live" I'll be happy to have a look for you.