Like in most countries, the political system of the republic of Austria consists of the judicative, legislative and the executive branch. The judicative branch is represented by the courts and the lawyers, the executive by the police and the bureaucrats, and the legislative by the two chambers of parliament. There also are three levels of laws: federal laws, state laws and regional laws. Constitutional laws (in the rank of federal laws) have to be issued by a 2/3 majority in the National Assembly, the "Nationalrat".
Similar to the USA, Austria has a federal Government. The territory of the federal republic is made up of the territories of the nine federal states, constituting a uniform monetary, economic and customs entity. The official head of the country is the president (currently Thomas Klestil), but unlike to the US, he interferes little in everyday political decisions. His function is to appoint a new federal chancellor after the elections, and to represent Austria to the outside world.
The Austrian Parliament is elected every four years by every citizen age 18 or older. It consists of two chambers, the "Nationalrat" (National Assembly) and the "Bundesrat". While the "Nationalrat" is reviewing and passing new laws, the "Bundesrat" has only a controling function and almost never intervenes in laws the national assembly passed.
After the elections are held, the 183 seats of the "Nationalrat" are split in proportion to the percentage of votes a party made, yet there is a minimum of four percent for a party to get some seats. This allows small parties to participate in the political process, yet ensuring that the number of fractions is not overly high.
In the two month following, the leaders of the parties will then meet to form a coalition with another party. The president will appoint a new chancellor, usually the leader of the party with the most votes, and further appoint ministers following the chancellors recommendation. If the party with the most votes is not able to form a majority-founding coalition, it can either rule with a miniority of seats, so it has to search for supporters for every law they want to pass, or it passes it's opportunity on, and the president appoints another chancellor.
After the decision for the new Government was made, the new parliament has it's constituting assembly and elects the first, second and third president of the "Nationalrat".
The incumbent Federal Government, the cabinet of the federal chancellor Wolfgang Schüssel, has been working since February 4th, 2000 on the basis of the Coalition Program between the Austrian People's Party and the Austria Freedom Party signed on February 3rd, 2000. According to the results of the elections in november 2002, where Mr. Schüssel made 42% of the votes, he most likely will be the head of the next Government.
Update from March 2003: The new government of Mr. Wolfgang Schüssel was inaugurated 2 weeks ago. He continues his coalition with the weakened freedom part (headed by vice-chancellor Herbert Haupt).