Snopes is your friend. Even if you cannot remember the site, searching for a sentence of a text probably will pull up a hoax clarification site.
Facebook is the new chainletter forwarding medium. The share button allows people to very easily and simply pass along anything. Often this is before they do anything to verify the information. Before anyone I know who reads this comments, I have been guilty of it too. I like to think it rarely happens.
Almost as long as I have been online, I have fought back against this kind of misinformation. When I see factual claims, I try and verify them. My GoogleFu is strong because of researching things I read or hear to confirm, deny, or better understand. If claims were false, then I left a comment. Initially I wrote in my own words detailed explanations on why something was in error. Then as I got lazier, I quoted places like Snopes who probably wrote better explanations anyway and linked back to the source.
These days at my laziest, I just post a link to the source.
Usually, I received a comment back in thanks. Sometimes it hurt feelings for me to have sent these comments. People have even stopped talking to me over getting a comment. The interesting ones involve me being called a liar or mean. So I pull back for a while and try not to hurt feelings. Eventually, I will resume responding.
Something I really should remember is people love their biases and these shares are part of solidifying them. I probably ignore the things with which I agree. By trying to correct them, I am fighting against cognitive dissonance and am not going to win.