Research the man first to gain an understanding of his life and times. Use reference material such as an encyclopedia, biography or literary publication article. Taking a short amount of time up front to gain Plato's insights will be an indispensable aid to reading and interpreting his philosophies.
Take a moment for a visualization exercise on the venues of Plato's time. This will help to formulate a good reviewing format. In ancient Greece, learned discussions were not held in indoor forums or courtrooms, but rather in open spaces in the middle of a city marked by freestanding colonnades or, ideally, near a harbor for the widest exposure to the issues at hand.
Make notes of names, dates, ideas and other details for use later when writing the review. Use a pen and paper, or a PC, to do this. "The Republic" is composed of 10 parts or books, each dedicated to a certain idea of the whole.
Break up the topic structure to echo how the debates may have been presented. In books I through IV, for example, Plato discusses the vision that he has for a city and the direction that it should take. Prior research into the man and his times will be helpful here. An analysis of Plato's intent to inspire change should reflect his earnest delivery, which would have been as solid as the platform he stood on -- and as lofty as the open colonnade he gave voice from.
Continue on with books V through VII to examine the natural flow of Plato's thought, which is a comparison of the contemporary city to a higher-quality utopian society. Describing these ideals, with personal opinion added to scrutinize his argument of the preference of a unified civility, is a good review strategy.
Include a critique on the forms of government that cannot sustain themselves, such as a tyranny, as well as a look at the makeup of a city's citizenry (including a human soul and the impact of art on the psyche), which books VIII through X discuss.
Take a day or two between finishing "The Republic" and starting a review of it. This breathing space is recommended to better understand its concepts and abstractions. Keeping in mind Plato's original purpose of this work will be a sound guide for analyzing its strengths and weaknesses and the effect it has had throughout the course of history.