Government Types
Absolute Monarchy - Exactly what it says on the tin. You as king rule with the closest the game comes to representing as absolute power. You can appoint parties that are Liberal, Conservative, or Reactionary, but do not have elections. Most countries begin the game as an AM.
Prussian Constitutionalism - This is a title made by Paradox for Vic2 to represent the 'grey area' between an absolutist monarchy and a constitutional monarchy. Essentially, you remain as king with large amounts of power but are slightly balanced out with elections. You can appoint party and have elections. Most western absolute monarchies transition to PCs around 1860-1870. Socialists are now added to the list of appointable parties.
HM's Government - This is Vic2's representation of constitutional monarchy. You still can appoint parties, but you have elections and many political reforms. HM's Government also allows you to appoint every ideology in the game.
Presidential Dictatorship - This is a catch-all term for a dictatorship without a hereditary head of state. As such, PDs can represent everything from banana republics to military dictatorships. You can only have reactionary parties in power, and there are no elections. This government can easily transition to democracy, if you are so inclined.
Bourgeois Dictatorship - This is the closest you'll come to having no government at all. I can't really come up with any historical examples of a BD. You can only have an anarcho-liberal party in power, and there are no elections. Avoid this government like the plague since it forces you into using Laissez-Fair (worst economic policy) with none of the bonuses of the other authoritarian governments.
Proletarian Dictatorship - This government represents your average run-of-the-mill totalitarian Communist state, the Soviet Union being the best example. You can only have Communist parties in power, and there are no elections.
Fascist Dictatorship - This covers all of the myriad fascist and quasi-fascist governments of the world, ranging from Mussolini's Italy to Franco's Spain to Nazi Germany. You can only have Fascist parties in power and there are no elections.
Democracy - This is a very broad governmental category that represents a democratic state with no hereditary monarch. As such, this can cover everything from hippie utopias to rather authoritarian states where only the aristocracy and capitalists can vote. You cannot appoint parties, but have elections. All political parties are allowed.
How to Get These Governments
Revolution: Typically, the government type that a rebellion wants is somewhat evident from their name.
Communists (Red Guards) = Proletarian Dictatorship
Fascists (Freikorps) = Fascist Dictatorship
Reactionaries (White Army) = Absolute Monarchy (if monarchy or presidential dictatorship) or Presidential Dictatorship (any non-monarchial gov.)
Jacobins (Republican Guard) = HM's Government (if monarchy) or Democracy (if HM's gov. or other type)
Anarcho-Liberals (Citizen Guard) = Bourgeois Dictatorship
Reform: Reforming your government is a longer process than revolution, but leaves your country far more intact and stable. You reform by having more than 50% liberals in your Upper House, though 25% of socialists will also vote for political reforms. If you want to go straight for changing your government type, than I recommend reforming Voting Strata and Upper House Composition first.
Reaction: On the other hand, if you want to make your government less liberal, you'll need at least 50% reactionaries in your Upper House. My recommendation for changing gov. type stands the same as with reform.