How can I compare the political systems of two states? I have to use at least four dimensions of the political system and find correlations between...

Although it is slightly ambiguous, I will assume the question isn't specifically referring to the US. Hence, by "states," the question is not referring to US states (e.g. Ohio, California, etc.), but to nation-states (e.g. United States, South Africa, China, Brazil), or what is commonly called "countries” in the US.

One way to think about the dimensions of political systems between states is to bracket your investigation into solely "democratic regimes." Within the political system of democracy, there are multiple dimensions of variability including the make up of the executive branch (head of government or head of state), the legislative branch (unicameral or bicameral), the judiciary branch (concrete or abstract review), legislative-executive relations (parliamentary or presidential system), and electoral systems (multimember districts or proportional representation). In addition to democracies, other political systems include those such as personal dictatorships, military regimes, one-party regimes, theocracies, communist regimes, corporatism, clientism, and totalitarian regimes.

One way to think about political performance is to think about the intended functions of particular political structures. Many textbooks use the following dimensions as a classification/evaluative schema: 1) political socialization, 2) political recruitment, 3) political communication, 4) interest articulation, 5) interest aggregation 6) policymaking, 7) policy implementation and adjudication.