I actually saw a very bright young college grad fall for this scam a few years ago.
It goes like this: You get a phone call from someone who says is name is so-and-so (Mack, Jack, Mike, Matt, Joe or what-have-you), and that he's with Microsoft Support or Windows Tech Support—something along those lines. He may speak with a thick accent.
He'll tell you that your computer is showing up on his monitor as being infected with a virus and that in order to prevent something really awful from happening to your data, he's going to help you fix it. Typically, he'll direct you to a web site and may even offer to help you change settings in your browser configuration (e.g., a proxy server IP address) if the site appears to be blocked.
If the conversation gets this far, it is way past time to hang up. Never, ever make changes to your security settings or navigate to a web site URL given to you by an unknown caller. Oh, and they may continue to try to call you at least once more before giving up.
Microsoft does not make unsolicited calls to help you fix your computer.
In fact, if anyone calls you claiming to represent some established corporation, retailer, charity, or government agency and then asks you to either (1) navigate to a web site, or (2) provide a credit card number or other personally identifying information, just hang up. Never give your information to an unsolicited caller, even if he says you already have an account with his organization. That's called social engineering; don't fall for it.
For more information about the tech support scam, see this page at the Microsoft Safety & Security Center: Avoid scams that use the Microsoft name fraudulently.