If you look in your programs list (from the Start menu), you'll probably find that alongside Norton, there's an 'uninstall' option. If so, that's what you should use.
Otherwise, you need to use the Add/Remove programs function. In pre-XP versions of Windows, it's accessed from Start > Control Panel. In XP it will be somewhere similar but probably a bit harder to find. (You can guess that I'm not a fan, or user, of XP!).
Once you've uninstalled the older version of Norton, you can install the new one but I have to ask the question, WHY?
Norton costs money. You can protect your PC just as well for free, by using a combination of AVG Free Edition (as your anti-virus software) and Zone Alarm Free Edition (as your firewall):
http://free.grisoft.com/doc/1
http://www.zonelabs.com/store/content/company/ products/znalm/freeDownload.jsp?dc=12bms&ctry= US&lang=en
Chris