I recall that this came up in #pirateradio a month or two ago. I did some research at the time, and one thing that came up was that these people were apparently preying on the elderly, in particular. In fact, there was some speculation that they had gotten ahold of an AARP mailing list.
Their procedure is to try to get the victim to enable remote access on their computer, in order to install a Microsoft update, or otherwise fix some problem that Microsoft had discovered with their computer. Of course, once the victim did this, providing access information such as the admin password to the caller, their computer would be owned, along with any and all personal information held on it.