In a quick nutshell. There's two extremes of survey taking. Qualitative or quantitative.
Qualitative surveys involves less people, but more in depth questions and follow up questions. The upside is you get more developed answers. The downside is that your survey sample is so small it might not be an accurate population representation and it takes more time to comb through the data and get results.
Quantitative surveys involve more people, but less involved questions. The upside is that you get a larger population sample, hopefully better reflecting public opinion, and it's easier to go through the data and compile the results. The downside is, sometimes the answers really do lead to ambiguity.
That's not factoring in problems like interviewer effect, poorly worded survey questions that can skew answers (deliberately or not), researchers mis-representing data, and of course, the media taking results and representing them in a way that was not intended. That said, from what I understand, Pew Research is pretty reputable and tackles all sorts of questions, which is probably why they're referred to a lot in the news.