There are a number of places that someone wishing to have a deeper understanding of politics American-style might choose to dive in. But one insight is far more important than all the rest: the ideologies of the left and right are not equal and opposite. While the left is ideologically committed to finding the empirically best policies, the right is ideologically committed to the belief that certain principles are more important than empirical reality.
Way back in February of 2005, Jonathan Chait in a piece called "Fact Finders" in The New Republic, identified and articulated this important difference:
Conservatives believe that big government impinges upon freedom. They may also believe that big government imposes large costs on the economy. But, for a true conservative, whatever ends they think smaller government may bring about--greater prosperity, economic mobility for the non-rich--are almost beside the point. As Milton Friedman wrote, "[F]reedom in economic arrangements is itself a component of freedom broadly understood, so economic freedom is an end in itself."
We're accustomed to thinking of liberalism and conservatism as parallel ideologies, with conservatives preferring less government and liberals preferring more. The equivalency breaks down, though, when you consider that liberals never claim that increasing the size of government is an end in itself. Liberals only support larger government if they have some reason to believe that it will lead to material improvement in people's lives. Conservatives also want material improvement in people's lives, of course, but proving that their policies can produce such an outcome is a luxury, not a necessity.