Main schools of economic thought in the U.S. and the U.K. are Keynesianism, Monetarism and Austrianism (and, increasingly, neo-Monetarism). Keynesianism is the most "liberal" of the schools, and you'll usually find it's adherence in the Democrat/Labour Party arguing against austerity and for more government spending, especially during a Recession, and adhering to a view of monetary policy focusing on interest rates. Keynesianism essentially gave us the idea that wages are sticky (this in downturns, you get unemployment instead of lower wages).

Monetarism is a more conservative/libertarian school of thought, and it was founded by Milton Friedman--who influenced both Reagan and Thatcher, although it's difficult to say how much they followed his advice. Monetarism agrees with Keynesianism that recessions are caused by inadequate demand (spending), but disagree as to the role of government. Unlike Keynesianism, Monetarists think inflation is more important to control than unemployment and believe that the money base (total amount of money in the economy) is the best indicator of monetary policy. It's no surprise that Monetarism influenced politics in the 80s, as the 70s had seen high unemployment and high inflation that Keynesianism didn't predict. However, Monetarism has also seen a decline since the 1990s when inflation and the growth of the money supply didn't happen on a one-for-one basis.

Austrian Economics is where you'll find the strong libertarians and hard money nuts--think Ron Paul. It was founded by Ludwig von Mises and F.A. Hayek--although there's definitely more Mises in the school today. Austrians have made some significant contributions to mainstream economics, but their disdain for empiricism and macroeconomic models has led to significant criticism. Austrians often argue for an unregulated market, a gold standard and think recessions are caused by malinvestment when interest rates are kept too low.

This is probably a bit ramshackle, so I'll answer any questions you have.

a gold standard

tfw you used to believe in that nonsense.

I still consider myself an Austrian, but I haven't come across one arguing for a gold standard in a few years.