I am almost certain it's not a fair question, as I think the most honest answer is simply, "I don't know. I just choose to believe some things are true and others false." Not exactly the kind of statement that warms the heart of my fundamentalist and evangelical instructors, but I have no idea how to achieve certainty about things that matter.
Students typically talk about facts or things that can be proven, even sometimes conflating those two categories. It does not take long to show how those categories are not always related, but I will allow that certain facts and things that can be proven are truths of a sort. One of the more outspoken adult students in this particular class offered, "Experience," as an answer.
"What do you mean," I asked.
"You can experience truth," she said.
I didn't think she was talking about some rudimentary form of emotivism, so I took a chance. She is probably late 50s, African American, bright, extroverted, and like me, sometimes too outspoken.
"Can we make this about race?" I asked.
She laughed, and said, "Of course."
Here's a rough paraphrase of what I said. Minority communities are far, far better at recognizing large-scale cultural lies than hegemonic communities, and that is because they live an experience counter to the cultural lie. For example, if we talk about America as a land of freedom and opportunity for everyone, people in minority communities immediately recognize the myriad ways that truism is not quite true. Yes, it can be true in limited circumstances, but across the culture, minority communities see that they do not have the same kinds or amount of freedom as hegemonic communities. Their experience is one that is lived as a lie according to the hegemony, but their experience reveals that the cultural truth is in fact a cultural lie, and their experience is in fact more true than the large-scale cultural truth. In this way, experience can lead us to a form of the truth. Minority students in the class readily agreed, but some of my white students looked irritated.
Yet another student talked about the Bible and sacred speech. This one is tedious, but can easily be handled. We talked about pluralism and what the collision of different cultures and religions had done to certainty. If I line up the Qur'an, Bible, Tanakh, Vedas, Upanishads, Dianetics, New World Translation of Scripture, Book of Mormon, etc., what criteria can you offer that will show me that one is superior to all the others? Which rubric should I use to discover which book reveals the truth? It's relatively certain that they all reveal some truths, but to say one is more true than others requires massive assumptions that have more to do with preference than epistemology. Even if we eliminate the really bad books, like Dianetics, we are still left to sort through competing claims with zero meaningful criteria to determine which book reveals "the truth." This is the nature of metaphysics, of course, but typically people in communities of faith are not told this.
As for sacred speech, whether prophecies, sermons, etc., they suffer from the same problems as sacred texts, with the added problem of verifying the authority of the speaker. Honestly, sacred texts have authority because a community says so. There is nothing intrinsically authoritative about a book, even if, and this makes me shake my head every time I hear it, the books say so. But sermons suffer from yet another problem. The sermon functions in many communities of faith as an exposition of the authoritative texts, so the authority of the speaker is tied directly to the community's affirmation of the text's authority and their trust in the character and honesty of the speaker. What I discovered over the many years of preaching and teaching I did in churches was that confirmation bias, either overtly or subtly, was at work in the communication dynamic between speaker and congregation. If I said something they already agreed with, it was an immediate nod of the head or "amen," but if I said something they had not considered before that didn't seem to conflict with what they already believed, they were still content with what I said. It was only those times when I said something that made them uncomfortable that I was confronted after a sermon, and usually, the congregant disagreed kindly. The transformations came from reinforcing things that the people already believed, things that were in fact good, not useless (like belief in angels or Rapture), thereby encouraging them to walk out the "truth" in their own lives. There is no path to truth in the broadest sense in sacred speech either, it seems.
We are left to wonder how to recognize truth, and I still don't have a good answer. I still haven't heard a good answer. The axioms seems clear, at least at a pragmatic level (assuming we're not deceived by a demon or some other Cartesian nonsense), so A really is not non-A, and while that is important, the truths we can't know seem to be the ones we are most at odds about and the ones most likely to cause conflict and violence.