What they do is poll a sample of the public. Polling organizations like Rasmussen or Gallup call about 3,500 people a week who are supposed to represent the public proportionately - calling different people every week - and they ask them questions like, "Do you think the president is doing a good job?"
There are actually about thirty fairly credible polling organizations, and many of the media networks will average the results.
It's still a little uncertain, though. The results are a statistic more or less, and we still see bias in the results. The people that the different organizations decide would represent the various parts of society can really change the outcome - sometimes drastically.
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