how do the tv stations know how many people are watching their shows?

They use a system called the Nielsen Ratings. Basically the Nielsen group installs their boxes in X homes (I forget the number, 10,000, 100,000, its a lot, but I still think inadequate). They monitor what those homes watch. They then use a bunch of math on those figures and come up with the Nielsen Ratings (or number of people that watched each show). Its a lot like political polls, just a bit more sophisticated (or at least said to be more sophisticated).

A lot of people criticize the system. But no one has come up with something better, and the networks are content on continuing to rely on it. So for the time being, its where those numbers are coming from.

Dats a good question I wud like to kno too

wikipedia

http://en.wikipedia.org/wiki/Nielsen_ratings