It is basically a fact of modern life that Facebook is a huge source of news and social interaction. Put those two together and disagreement and debate are all but inevitable. I even recommend seeking it out and being vocal about what you believe. However, Facebook disagreements can easily dissolve into trolling, ad hominems, and generally a terrible time for all involved. I come from a background of debate, I even wrote some general guidelines for a formal debate, but Facebook is a very different animal. The nature of comments is that they are relatively short (although I've certainly seen and written ones that were small essays) so some information and nuance is bound to get lost in the medium. There also aren't any moderators or anything to regulate the debate to keep it on topic and civil. So, how can you have a good debate on such a platform?
In short: Don't even try.
However, if, like me, you're stubborn and insist on having them anyway, heed the following.
1. Know your audience!
I don't necessarily mean the person whose post you are commenting on, I mean the people you want your comment to reach. If you are looking to persuade the person who posted, that's fine, but keep that in mind when you're writing. If your comment is for the emotional release of getting something "off your chest", that's fine so long as you know that's what you're doing. If, like me, you comment for third parties that are going to be exposed to the post and the comments on it, then you have to write with that information in mind. This doesn't really change any of the other tips, but it does give them a bit more context.
2. Keep it civil!
What is put on the internet, more or less, stays on the internet. Whatever you say, make sure you're okay with friends, family, and future employers being able to see what you said. More than that, incivility will lead to a discordant discussion faster than you can compare someone to Hitler. This includes calling out incivility. You can disagree quite vehemently with someone without resorting to insults of ill wishes. I say this as someone who has been told, implicitly, that they are going to hell while discussing something on Facebook. When that happens, even if I agree with the person's argument, I make a point of keeping insults out of the discussion.
This does not mean you should tolerate intolerance. If someone is being intolerant or hateful, especially without factual basis, feel free call them out on it. I've done so with liberals and conservatives, so don't hesitate to call hate what it is and point out where it is unfounded.
3. Respect evidence!
Regardless of where you stand on a given issue, we all should respect numerical evidence over anecdotal experiences. Anecdotes, by definition, are personal experience. Statistical data, collected by professionals, is far more revealing of what actually happens in the world. For instance, just because you may have had a really good or really bad experience with a given car brand doesn't mean the brand is good or bad as a whole. For that we have to look at objective measures such as resale value, fuel efficiency, customer satisfaction rating, etcetera. Another way to look at it is sample size. An anecdote is a sample size of 1, even if you have a dozen anecdotes that still only brings you to 12, but most empirical studies or surveys have sample sizes of 100 at least. Polls in particular tend to reach thousands of people.
4. Be willing to be wrong!
If you aren't willing to believe that you might be wrong on a factual point, then everyone is in for a bad time. Matters of opinion are a different issue where disagreement is almost never actually going to be resolved. When confronted with factual evidence that your position is incorrect, be willing to change.
5. Know when to stop!
There are going to be times where discussions aren't worth the trouble. It might be because someone is actively trolling, or perhaps the ideological differences simply can't be reconciled. Regardless of why, know when to cease participation in a conversation for your own sake if nothing else.