Well, for starters (given two-way communication) you can ask them for the sources of their claims, or at least demand that they defend the logic behind it. Then you can take it from there, and unravel the fallacies for them. Or if you want to be more polite, then carefully point the fallacies out for them and ask what they think about it themselves, when looking more closely at it. This would be the pedagogic approach, for those of you who have the patience.
And if it all falls apart (like it sometimes does when people are faced with their own failure), then you can at least ask them to give arguments instead of ad homs. I always try to be polite the first time around, but if they double down, I let them have it. But really, if it ever falls that low, it usually means that you already won, and so you don't really need to bother any further with the discussion.
My thinking is that most people who read such discussions can think for themselves, and so giving good arguments, unraveling faulty logic, and showing the truth, will always let truth and logic prevail in the end.
Usually you will never get a person to admit that he's wrong anyway, at least not to your face, so don't even worry about it! But people do change their minds about things. It usually happens in private, especially if they just facepalmed right into their own flawed logic. So if they do, never gloat and pretend like nothing happened, and rather commend them for telling the truth later on.
Perhaps I'm naïve, but I enjoy staying positive like that. :)
Mere faceless fake news and conspiracy theories, however, simply needs highlighting and debunking. There are several sites that specialize in that already, with various success. It's not perfect, but IMHO it's preferrable to outright censorship. Because who can be the final arbiter of truth anyway...