They are calling as many as they can, either from voter registration, phone book, or other sources at random. I would guess they get a live answer 10% of the time, and of those who answer, 10% agree to do the survey. That means for 1,000 respondents, they probably had to dial around 100,000 numbers. This is why it takes several days or more to do the survey. Much of the demo breakdown comes after they answer those questions (so depending on the source, they don't always know in advance what age groups they are getting before they call).
Of course, they also know which numbers will reliably be answered by the drunk 65 year old that lives in front of Fox News while their houses are falling down around them and only their government checks keep their bellies full of GMO and fortified wine.