How long does it take to watch a TV show for it to be considered "watched" by the Nielsen rating system?

You have to be part of the Nielsen program, as I understand it, which includes a box provided by Nielsen that transmits the information. Unless they’ve changed the way it works, if you didn’t sign up, they don’t know what you are watching.

Actually, I think it used to be an actual written survey.

Unless you are a Nielsen family, you would know if you were, then your television viewing isn’t recorded. It’s borth a transmitter box on your televison and a written survey. Any amount of time is recorded. The analysis is done minute by minute.

See this link http://www.howstuffworks.com/question433.htm

@gussnarp & @saranwrapper Oh, I didn’t know that. How many people are part of the Nielsen family?

And do they get paid for this?

They don’t get paid. They just get to feel important. According to @gussnarp‘s link about 5,000 households participate yearly.