Epistemology is the discipline which investigates claims to knowledge and epistemologists, among other things, try to layout systematically why it is they think they are justified (or warranted) in claiming to know certain things.
Of course, just like in metaphysics, there are those who are skeptical that such a project can be done, but the quest for epistemic justification (or warrant) is an on-going project even today. In the modern philosophical period there has been two main streams, the rationalists who insist that we do not know changing things and only know unchanging concepts and forms, and the empiricists who by contrast claim that all we know directly or by extension are those things which have or have had an empirical (experiential) impression on our minds.
The Enlightenment arguably tended to endorse the empirical methodology, but some were convinced that both rationalism and empiricism led inevitably to skepticism. Immanuel Kant sought to rescue that alleged situation by seeking something of a compromise by holding that what humans were equipped to know were the things as they (empirically) appear to us, but that humans were not (necessarily) equipped to know things in themselves.
The current debate in epistemology has centered on two different sort of schools of thought, the so-called internalists who hold that what counts for warranted belief is, as it were, internally available to knower and that it is her duty to form beliefs rationally. Whereas the externalists hold that at least for some beliefs, what counts for warrant is not directly available to the knower--they are external to her--and thus some belief formation is beyond her control. Just how this plays out theoretically remains (as you can imagine) a theoretical watershed.
The readings and on-line resources in this section should help you grasp important notions in epistemology and better equip you as you think through how these lessons can apply to your apologetic stance.