I believe that one good way to do it is to constantly ask yourself “Why do I feel this way?” and encourage yourself to question all of your beliefs. To question everything, before you even come to believe a particular thing.
It also highly depends on what someone is being “cynical” about. If it’s their own life, they get the final say on whether or not their viewpoint is justified, because they’re the ones who experienced it. No one has the right to enter someone’s life and tell them “You’re looking at it all wrong”, because no two people have the same experiences – even when they’re extremely similar. Not everyone’s brain processes experiences the same way, and so, even two siblings who grew up in the same environment might turn out as opposites because they learned to cope differently.
If you’re talking more broadly, about a worldview, well… that’s not so easy to answer. As someone who is frequently labeled “cynical” by a lot of people (I disagree and say that I am very much a realist), I simply say “If I’m cynical, why then, is there so much horror left in the world? Why, if my feelings are not justified, is there still so much to fix?”. And that’s just it – those who think the world is more good than bad aren’t driven to make it a better place, because they don’t see anything wrong with it. So regardless of how I or anyone else labels me, it is impossible to acknowledge (unless someone is just a moron) that there is still plenty to fix.