First, just plug your webcam into the computer and see if XP can install it. XP is very good at that sort of thing.
If that doesn't work, go to
this Logitech page, click on your model and see if they offer any downloads for it. If you don't see your model, click on "Other" for more listings.
If you don't know whether you have an antivirus software, look in Control Panel>Add and Remove Programs for "Symantec" *(or "Norton," which is owned by Symantec) or "McAfee"(those two being most commonly bundled with a preinstalled system). If you find either of those installed but you haven't paid for a subscription, it's a trial version, has expired if your computer is more than a couple of months old and is therefore useless.
If that's the case, you can get AVG from
www.grisoft.com. It's a free antivirus program, works well and doesn't hog resources.