How does the mind build a model of reality?
Taking @BenCole's suggestion on the bolded parts...


  how the human mind creates and perpetuates the idea of knowing something


I think the philosophic response to this is "What does it mean to know something?". I'd recommend Searle's Chinese Room argument [1] and the many rebuttals to it (which include some computational explanations of understanding) to get a better idea.


  Do individuals build their own models of reality from whatever knowledge is available to their minds?


The simple answer is yes. But the interesting question is how much of our reality is shared vs how much of it is specific to each individual. In Computational Cognitive Science, the one area that tries to address this separation is Cognitive Architectures. CAs divide rational thought into two parts - the architecture that represents the common functionality across all humans and the knowledge which is different for each of us. For further reading, see Newell's Unified Theories of Cognition [2] for the groundwork, Anderson's How can the human mind occur in the physical universe? [3] for an emphasis on ACT-R (an example CA), and Laird's The Soar cognitive architecture [4] for an emphasis on Soar (another CA). Soar and ACT-R are the big two of the CA field but there are many others. 


  present a finite understanding of a infinitely(?) complex reality as complete.


I'd argue that the opposite is true. That is, instead of presenting reality as complete, the  mind lives off of the differences between its understanding and the reality. Expectation-based cognition suggests that people are always generating expectations of what they expect to sense (see/hear/smell/feel etc) in the near future. These expectations are matched against observations. If expectations and observations match, then all is good. When they don't match, cognition is alerted. In this view, predictions flow top-down and errors (discrepancies between the prediction and the observation) flow bottom-up. Some good references on this idea are [5] and [6]

[1] J. Searle. (1980). Minds, brains and programs. Behavioral and Brain Sciences 3 (3): 417–457.

[2] A. Newell. (1994). Unified theories of cognition. Harvard University Press.

[3] J. Anderson (2007). How can the human mind occur in the physical universe? Oxford University Press.

[4] J. Laird. (2012). The Soar cognitive architecture. MIT Press.

[5] Lee, T.S., Mumford, D. (2003) Hierarchical Bayesian inference in the visual cortex. Journal of Optical Society of America, A. . 20(7): 1434-1448.

[6] Hohwy, J., Roepstorff, A., &amp; Friston, K. (2008). Predictive coding explains binocular rivalry: an epistemological review. Cognition, 108(3), 687-701. ELSEVIER SCIENCE BV. Retrieved from http://discovery.ucl.ac.uk/136548/