In many ways, Politics is a companion volume to the Nicomachean Ethics, in which Aristotle defines a life of good quality and sets about describing how it should be achieved. Politics, to a large extent, is an effort to describe the kind of political association that would best facilitate the ends described in the Ethics.
However, Politics is not subservient to Nicomachean Ethics. Aristotle's claim is not that cities must exist to serve the ends of individuals. Rather, he claims that individuals are to a large extent defined by the cities they live in and that man can be fully human (i.e. fully rational) only by participating in the city. The city is a complete whole and each individual is a mere part. The city is thus more important than the individual.
The tension between practical and speculative reasoning is central to the Politics. Practical reasoning is necessary for political and social matters, while speculative reasoning is necessary for theoretical and philosophical problems. Ultimately, Aristotle concludes in both Nicomachean Ethics and Politics that speculative reasoning is superior, as it is through a proper exercise of this faculty that man achieves true happiness.
Whereas Aristotle views the exercise of speculative reasoning as and end in itself, he considers the exercise of practical reasoning an integral means to this end. Because an individual cannot learn to exercise his reason properly outside the confines of the city, and because the city is able to function only as a result of man's practical reasoning, practical reasoning is thus a prerequisite for the exercise of speculative reasoning.
Interestingly, Aristotle never concerns himself with questions of how much authority the state should have over the individual. A central question of modern political philosophy is the extent to which the state should be able to impose itself on the freedom of the individual. This question would not have made sense to Aristotle because he saw the goal of the city and the goal of the individual as identical. While his assertion—that the individual is only a subservient part of the state—might seem mildly totalitarian, his view was that the individual could have no truly rational needs or interests outside the confines of the state. As a result, it would be absurd to desire any kind of individual freedom in opposition to the state.
"Justice" might seem an odd term for what is essentially the right to hold more distinguished public offices. It is important to remember, however, that in a Greek city-state, serving in public office was essential to citizenship and was a high distinction. Further, those who occupied places of high distinction were more likely to enjoy other benefits as well.
Aristotle's method, here and elsewhere, is largely descriptive. He conducts extensive surveys of the different forms of government and theory and his own theory is less of a creative endeavor than Plato's in the The Republic. Rather, it is a series of recommendations based on what he has observed. None of Aristotle's practical advice is particularly novel; his insights are more a synthesis of analyses by a man who has studied politics extensively.