Theo, Nielsen uses a combination of methods, but it is a large sample selected to reflect the U.S. demographically, and the actual people in the sample are rotated every few years. IIRC it's one third every year. The people meters are used and every person in a household participate.
Nielsen also uses a diary sample in addition to supplement the overall sample for sweeps periods, i.e., a large sample to measure each local market.
There are other ways to measure time shifted viewing, i.e., data from cable and satellite providers and the various streaming services, which come into play for mobile devices smartphones as well as TV, that are used for live plus three (days), seven days or 30 days.
One thing to keep in mind is that the networks no long pay much attention to the overnight (live plus same day) numbers, only the media uses them. The size of the live audience for virtually all shows has dropped tremendously as measured overnight, but that trend is deceptive due to a lot of factors, such as a broader range of choices on cable and streaming services, and the ever increasing growth of time shifted and cord cutting viewing. Except for sports and live coverage of breaking news events, the shrinkage in the live audiences for broadcast shows has been significant and noticeable. So far this TV season the shrinkage has been roughly 15 - 20%, and TAR was one of the few to be even with last year.
