By plane - Vienna’s international airport -- Wien Schwechat -- is about 20 km south-east of the city. Regular buses link the airport with the center. Buses leave from right outside the arrival hall. They go to the city’s Südbahnhof, Westbahnhof, and Wien-Mitte train stations. A one way ticket costs 5.80 Euro.
Taking a cab to the center should cost you around 25 Euro. Generally, in Austria taxis are safe and reliable.
The usual car rental agencies also have their offices at the airport.

For more information on Vienna airport, check out its homepage:
http://english.viennaairport.com/

By train - Most international trains go to the city’s south, west, and east train stations. Vienna has direct train links with major European cities. Trains from Paris, Munich, Salzburg and Innsbruck arrive at the Westbahnhof. The Südbahnhof and the Ostbahnhof are placed under one roof near the Belvedere palace. From here you can go to Rome and many central and eastern European destinations. Trains from Budapest arrive either at the Süd- or Westbahnhof.

The Westbahnhof is conveniently linked to the city’s metro system (U3 and U6). From the Südbahnhof and the Ostbahnhof you have to take either the tram (line D goes right to the center; the tram station is on the eastern side of the main building) or the Schnellbahn (trains leave from the station under the main hall).

You can have a look at the website of the Austrian Federal Railway Agency (ÖBB):
http://www.oebb.at/en/index.html