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Don't know how they do it for radio broadcasts, but for TV ratings (and I'd assume radio would have to work in a similar fashion) Nielsen contacts randomly selected families offering to install their hardware; on a day-to-day basis whenever a family member starts watching TV they press their own button on a remote control of sorts, so not only are the programs being watched logged but the specific person (for demographic distributions and such).
You are right in thinking that the whole thing is wildly inaccurate. They try to offset bias by randomly selecting the participants, but there's still significant bias agreeing to be monitored. You might have noticed that the word "family" gets repeated a lot, Nielsen intentially works specifically with family households, I am not sure what the reason for this is, but it seems like they are leaving out large swatches of the coveted "18-25 with disposable income" demographic.
Gallup and (blanking out on the name of the other big polling organization) have a similar problem, they randomly generate phone exchanges for their interviews, which leaves out temporary ones, like for example, university students.
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