If your kids MUST use Kazaa, get them to install Kazaa Lite from click here
The full-fat version is riddled with spyware and other nasties. Either way, update and then run Adaware and Spybot after you install it.
It sets up a shared folder into which by default anything downloaded is saved. You can add further folders which you're prepared to share, usually your music folder. You don't have to share files on your PC, but it's considered good P2P etiquette to do so, and you might find yourself blocked if you don't.
The only thing Kazaa Lite will search is folders you have allowed it to share - it shouldn't pluck other stuff off your drive, but then as I say, it's riddled with nasties and you should keep a very sharp eye on it.
Your firewall will have a fit and you'll have to set the permissions for it.
I'll leave the arguments about the legality and desirability to sharing copyright files to others. Suffice to say I've used Kazaa Lite successfully and with the proper protections in place - firewall, anti-virus softwae, regular scans for malware and other nasties - I've never had any problems.
Finally, though, don't do it on a dial-up: anything you download or upload will take forever.
Hope that helps ...