There are some winamp plugins that can perform this operation, but here is the general idea.
The assumption is that the vocals are generally in the midrange and are equal in magnitude in both the left and right channels or a stereo signal. Other instruments have higher/lower frequencies or are not "balanced" between the channels. The signal is filtered to obtain just the midrange (usually they allow you to adjust the passband corner frequencies). The common part of this signal is then subtracted from the left and right channels.
Having said that, I have found this method works, but is not perfect, you can somtimes here hints of the vocals.