Step one: Evaluate yourself.
Are you emotionally stable? Do you have enough energy for this conversation? Is this topic really important enough that it merits a mini-essay on why the other person is mistaken? If so, you may think about proceeding. Have fun.
Step two: Evaluate the conversation thus far.
Is this person open to reason, or are they dismissing anything and everything that does not fit with their worldview? Are they arguing rationally, or are they throwing around insults? Do they treat the opposing argument as though it were a dead animal rotting by the side of the road? Because if some of these these things are true, you’re gonna have a bad time.
Step three: Respond thoughtfully.
Watch your wording. Do not resort to insults or fallacies. Basically, be a decent human being–the kind you’d want someone else to be to you. The Golden Rule applies here, because every time the fight gets escalated, things become worse for you. And you probably don’t want that.
Step four: Observe their response.
If they do not, at the very least, acknowledge that you might have a point, there’s probably not much point in arguing further. It will only make everyone angry and cling to their views even harder, and that’s pretty counterproductive when you’re trying to convince somebody that they’re wrong.
Step five: Walk away.
Refusing to answer is not a defeat. It is an acknowledgement that there is no more point in wasting your time, your words, or your energy. You can consider it a personal victory in deciding when and where to spend your resources. Good job! Yay you. You’ve won.
Alternate plan: Ignore arguments completely. Watch amusing videos. Continue on your merry way. You are better than many of us. Congratulations.