One way the worm spreads is on USB flash drives taking advantage of the autorun feature. I explained the autorun tricks used by malicious software on flash drives and the best way to disable Autorun for protection from infected USB flash drives.
If you are infected, the free Windows Malicious Software Removal Tool from Microsoft can remove Conficker. I described how to manually have it run a full scan of your computer.
Another defensive tactic is using OpenDNS, which prevented the first two versions of the Conficker worm from phoning home for instructions from the head office. Registered users of OpenDNS are also told of any computers on their network that are trying to contact the Conficker head office. I don't know however, if this offers any protection from the third version of the Conficker worm.
Previously I wrote about DropMyRights, which can run software in restricted mode and offers great protection for Windows XP users.
Leslie Stahl says to buy security software. I'll be more specific. While not a specific Conficker thing, people keep saying good things about the antivirus program AntiVir from Avira. For the really nasty stuff, I'd put my trust in Malwarebytes' Anti-Malware.
Part of the focus of the 60 Minutes story is on new actions Conficker will take on April 1st. For more on that see Questions and Answers: Conficker and April 1st from F-Secure. They expect it to be a big nothing.
Of course, you can always switch from Windows to a Mac or Linux. I've also said here that I think children should run Linux.