I've been thinking about this since I watched the video that I posted in References here, the discussion between JP and Steven Hicks on postmodernism. JP describes a view of evolutionary epistemology and I agree with this view.
The idea is that our senses, cognitive capacities and "minds" generally have evolved through natural selection and would not have survived had they not been adequate to give us accurate information about the reality around us, accurate enough to enable us to survive and reproduce. The postmodern and skeptical anti-scientific criticism of that is simply to say things like "well you beg the question that there is even an outside reality, that evolution is true, that you even exist..." so obviously we can dismiss such criticism as irrational nonsense.
So to the question of how can we know that what we know and how we know is accurate or at least possibly able to be accurate, is clearly explained by understanding the conditions in which we have developed. I always say the same thing to radical skeptics, "if you doubt everything then go try eating a glass sandwich and see what happens". Or go try to walk out in the highway because you doubt that your senses are giving you accurate information about the oncoming cars (or you doubt that cars even exist). I'm sick of these radical skeptic idiots.
Anyway, I like evolutionary epistemology. It is a basic starting point for beginning to build an understanding that gets better over time, as we refine our ideas and our perceptions with philosophy and with technology/scientific method. If at basic our senses and cognitive capacities evolved only because they successfully model reality in sufficient degree to allow us to survive and thrive, and indeed this is the case, then at the bottom of our consciousness is not some kind of deep and unsolvable delusion, but rather the opposite: a deep connection to reality, to truth. We take this basic state and build from it, developing mind and critical thinking, using science and logic, testing hypotheses until we find ones for which no contradictions can be found.