Plato was a man who had his hand into a whole of pies in life. Interested in a whole lot of things.
Plato’s enthusiasm for mathematics, astronomy, and musical theory appears everywhere in his writings, and he also displays a far from superficial knowledge of the medicine and physiology of his day. (source)
Now I have to admit that I read that and I think of scripture where we know that what we have now is a dim shadow of what is to come. Isn't it amazing the Plato as a philosopher grasped this thought. This thought that we aren't perfect. We can't be. We all have the knowledge of God within us, but we aren't God, we aren't perfect, all we can do is strive after that...and then in the life to come... God will grant us new bodies and we shall live perfectly with him. In the meantime we are living in a world not our own, that nothing is perfect in because of the influence of sin in our lives.
Living in a world where we can't count on our senses means we have to count on our logic or reasoning.
Plato was careful how he documented his thoughts, writing in such a way that he left no definitive conclusion. He wanted to force people to think through the ideas on their own. Having a dialogue was crucial to learning and he developed the logical argument.
Plato, unlike Socrates was literate and wrote books : The Republic, the Symposium, the Phaedo, the Theaetetus; the Parmenides,and The Laws.
There is much much more to Plato, but this at least gives you some ideas about how his philosophical approach worked. :)