Plato compares a number of things in this essay--the material world of ideas, the life of the mind to the work of governing, silver and gold to virtue and wisdom. how does he use comparisons to make his argument?

By using comparisons he makes it easier for people to understand why his arguments are sound. An example can be his Cave Story which is in it's entirety a comparison, or an allegory, for finding ways to enlighten yourself and to see what the world is actually like.