The Soviets, and now the Russians, have been trying to influence U.S. politics for decades, primarily by influencing public opinion. And, not just U.S., they did the same all over the world. The most blatant way was to helping professors and intellectuals who were favorable to socialism. They would invite them to see how well their revolution was going, they would provide them with "data" about how well their economy was doing. It seems unbelievable now that Samuelson's widely used Economic text book kept projecting that the U.SS.S.r would surpass the U.S. in a decade a two... and continued to predict this through years of revisions.
Another thrust was the aiding of anti-war and anti-nuke movements all over the world. Along with that, they always had an eye out for disaffected groups in the west, and would help fringe groups if they were railing against the political system of the west. It did not matter if the ideology of such groups was counter to their own. In the eyes of a Russian KGB/FSB officer, a fringe group with a religious agenda or even with a radically free-market agenda is a potential asset. There's potential for such groups to spread dissent while never actually succeeding too much; but there are all sorts of related advantages in using local groups for cover and to lend an domestic legitimacy to other activities that may otherwise appear suspiciously Russian.
In the post Soviet era, semi-private organizations like RT work with this as their dual agenda. Social media opens another avenue. From their premises, the Russian FSB would be stupid not to use this new media, when it is available, and becoming the primary source of news for so many U.S. voters. It's also a place they have a slight advantage, because they are quicker to censor things they do not like. SO, they set up organizations to publish on social media, for a U.S. audience. Of course, "publish" means something different from traditional media. On FB, you have to create sock-puppet accounts, build networks of friends, build cred, and then start to send out the propaganda.
In the last election, the Russians seemed to have preferred Trump over Hillary, but that is in keeping with their usual playbook of disrupting the establishment. I doubt the potential policies of the two candidates was a big deal. And, apart from social media, they also influenced people in Trump's campaign, promising them dirt on Hillary, and possibly delivering.
U.S. Politics: None of this implies that Trump won because of Russian influence. Is it possible that he did? Yes, of course. Given the razor thin margin by which Trump won the election (only certain states matter in this calculus), and given how big a role Hillary's negatives played, it is possible that a small percentage in swing states might have voted differently. Even those voters themselves would not be able to tell you; so, it is an impossible question to answer either way. The only thing that makes it "possible" and plausible is the thin margins and the nature of the positives/negatives.
It is really bad strategy -- from the Democratic perspective -- to think that Trump won because of the Russians. If they truly think this, they won't address their actual weaknesses: the things that explain the bulk of the difference in votes. In my judgement, influential mainstream Democrats do not believe this. They understand that people wanted to chuck them out, and that they had a candidate whose core message was "more of the same". However, most Democrats are willing to spread this narrative because it is the only explanation that many party faithful will buy. This is short-sighted, because their best long-term solution is to re-position themselves a bit, for which they need to explain the real reason they failed. Instead, they seem to be hoping that the country will tire of the buffoon in the White house in 4 years. it's a gamble; but they've been in this game for a long time, and understand how difficult it is to change their members' ideology.
Back to the Russian menace: At heart, the problem with the country is the ignorant and confused American voter, who has mostly bought in to statism as a theory of politics. With such voters being the vast majority, they'll keep voting for statist politicians and cheering statist laws. Whether it's Trump or Hillary, ... that's not going to make any fundamental changes to the country.