KiddieToysReview gave a ton of great information, and as others have said there is a lot of luck involved, too. There is a viral video from 2013 called "Girl Learns to Dance in a Year (TIME LAPSE)". Currently, the video has 10, 019, 513 views, and the creator is even offering a viral service due to the success of the video, but when you check out the other videos on her channel the amount of views on her videos vary from three thousand to a million. So, even though she created a viral video four years ago, she hasn't been able to reproduce its success.
Another element of a viral video is what I like to call "the ego element". Because the determining factor of whether or not a video becomes viral is the sharing of the video, you need to give people a reason to share it. And what better way to get people to share a video than by stroking their ego. Have you seen those grammar/spelling/IQ tests that are all over Facebook? If you have, it was likely because a friend of yours shared it because they received a high score on the test (which in my experience it rigged). People like to share things that make them look good. So come up with an idea that will "stroke the ego" of your viewer and heavily promote it.
And tags are a very small SEO contributor unless the keyword that you're trying to rank is very, very low competition. Try to stuff as many keywords in the title and description as possible. But keep in mind that onpage SEO will only take you so far, the competition has to be pretty much nonexistent. For harder keywords you'll need plenty of offpage SEO.