It seems like that could be quite an important question to me.
This week, a lecture (on romanticism and theology - intriguing stuff) has got me thinking about the different factors that have an effect on my coming to know something. I'm sure there are loads, but I've been pondering six of them. I suspect that all 'coming to know' or acquiring knowledge involves a mix of at least these six things in different measures. And I further suspect that this makes the process much less straightforward than is often assumed. My six things were:
1. Sense experience. This is the 'given' of our knowledge, the stuff that is just external to us and over which we have very limited control. It is sights, sounds, smells, touch, taste - and perhaps other things too. But it is very limited by itself, being just sensations and nothing more.
2. Reason or understanding. We 'think' our world together into a whole. (Yes, this is Kant. So he wasn't wrong about everything). We don't experience pure sensation, but objects and scenery. That is a product of our brains putting our sensory information together.
3. Imagination. I'm thinking here of the way in which we tell the story of our lives. This experience, this thought, is not isolated, but fits into a pattern. Imagination tells me who I am, and where I have come from. Of course, this is not just me telling my story, although there is that. It is also me fitting my story into bigger stories, the stories of my culture, my religion, and the like. Just to clarify, I don't say 'imagination' because these stories are untrue, but because they are not 'there' in my experiences. The stories are a (necessary) way of construing and understanding our experiences.
4. Will. I believe things because I want them to be true. I am capable of resisting conclusions which appear to follow from my experiences, and of avoiding the obvious explanations to make my experiences fit different stories. As an aside, that is why in the Biblical narrative it is a sin, not just a mistake, to disbelieve in God. Again, this is not purely an individualistic experience. There is such a thing as a collective will, which expresses itself in expectations of belief and behaviour - what we might call, if it didn't have automatic negative connotations for us, peer pressure.
5. Memory. The storehouse of my previous experiences and knowledge is obviously a major source of knowledge, not only because of its basic contents but because of the connections and arrangements between 'things known' that are reflected there. Failure to remember - whether deliberate or accidental - is also, of course, important here. Again, not purely individualistic but includes cultural memory, often reinforced by ritual, like Remembrance Day, or the Lord's Supper.
6. Relationships. Much of my knowledge - indeed, most of it by a long way - is acquired from other people. Often in the process of coming to know something, my opinion of the person giving testimony can be the decisive factor in whether I adopt their point of view or believe that their testimony is fact.
Note that I haven't distinguished between 'coming to know' and 'coming to believe' in any of the above. I'm not sure I can think of any good way to do that. At least psychologically, there doesn't seem to be any difference. I know that there is a God; many people know otherwise. Neither of us would accept that our position is 'mere belief'. Besides, I think that language of belief is too often used to remove metaphysics and religion from the realm of what is 'really true' in a thoroughly illegitimate way.
Complicated, isn't it?