Answer by Jay Wacker:

1.) gather an immense amount of data
2.) perform relatively simple statistical analyses
3.) add expert knowledge to fix naive use of statistics

The only thing that Nate Silver (and a dozen or so different groups) showed is that the polls were accurate and treating them in a straightforward honest manner gives a more accurate answer than any single poll.

To be fair, Nate Silver corrected for numerous subtleties of the polls having to do with systematic bias, whether possibly intentional or not. They deweighted polls that were historically off or systematically disagreed with other polls.   However, all of this expert knowledge corrections they introduced was independently created by several other groups, showing that standard practices gave the right result.

The key thing about taking this method forward is that without the polls (he had hundreds of polls, each of which with thousands of properly sampled and corrected for demographic populations), Nate Silver had exactly bumpkis, which he would say as well.  The polls were his data.  Getting the data is expensive and hard.  Analyzing it correctly, if not easy, is something that hundreds of thousands of scientists are trained in doing.

So if you have extensive polling, I’d advise averaging them together combining them weighting them inversely proportional to their error.  If you have historical information, identify ways that the polls systematically skew and correct for that.   However, these events are few and far between.