Plato's theory of epistemology has something to do with his Theory of Forms. This theory states that there is a world in which there are perfect forms of everything. This perfect world is what gives everything their specific characteristics. He says there are sensible objects, what we can touch, and there are abstract forms. The abstract forms are the base for the sensible objects. Sensible objects are were we live, abstract forms are in the Platonic World. So this world is just an imperfect reconstruction of the Platonic World (the world of perfect forms.) 

About knowledge, Plato states that we have inert knowledge, we are born with the knowledge. This is because our souls lived in the Platonic World before being incarnated, so when they are incarnated they just go through a process of remembering everything. 
Plato also stated that our soul is divided in three, the tripartite soul: reason, appetite, and spirit. Appetite does not makes reference to the hunger part, but to the action os satisfying our needs like reproduction, food, drinking, sleeping, shelter, etc. The spiritual part of our soul is the one that gives us the courage of our convictions. And finally, reason, this is the part of our soul that makes us rational. Plato believes that reason should rule over appetite and soul, that's what being a person means. That's why for Plato, knowledge can only be acquired through reason, not by your senses, untested opinions, or feelings. For example, if you are playing volleyball and you are very thirsty and you see water coming out of some tube in the wall full with dirt particles you will probably don't drink it. Why? Our appetite part of our soul tells us to do so we can satisfy our drinking appetite, but that's when the rational part comes, you reason that the water is dirty and you will probably get sick, even die, so you decide not to drink it. 

We can use Plato's cave allegory also. This allegory says that we are prisoners in a cave attached to a wall. Behind the wall there is a fire and puppets that carry images of things. This fire makes shadows against the wall and that's all we can see. But these are just images, they're not what's real. In order to understand what's real we need to get out of the cave and see things as they really are. When you get out of the cave the sun will make your eyes hurt, but you will get used to it. After that you will see things as they really are. Now when you return to the cave to save the others expect hostile answers because they are inherited in their shadows world. Getting out of the cave is the act of philosophizing. When you are finally out, you can call yourself a philosopher. That`s another way of acquiring knowledge for Plato. 
Another way to acquire knowledge is the following. Before you can acquire knowledge of anything you need to understand the abstract form of that something. For example, a tree. You need to understand the abstract form of a tree, maybe leaves, a trunk, branches, etc. Now to acquire knowledge of something you need to have two different ideas, a coconut tree and an apple tree for example. Now that you understand the abstract form of a tree you can start comparing and thinking about these other two trees. Finally you get to a conclusion of how to differentiate each tree, and knowledge is acquired that way. 



This is Plato's epistemology theory.