It costs 3 euros to take the train from Vienna Airport to the Südbahnhof in the city. But for only 5 euros you can get a 24-hour ticket valid for all public transport within the city: buses, trams, underground trains. And if you stay out partying till late, you can always zip around in one of the city's many Mercedes taxis.
Vienna Schwechat airport is located on the south-west side of the city. There are trains and shuttle buses running regularly between Wien Mitte / Südbahnhof / Westbahnhof and the airport.
Getting around Vienna is easy. You can either stroll around as the city centre is not particularly large or you can buy the Wien Karte which allows you 72 hours of unlimited travel on public transport and also numerous discounts for museums and other sightseeing spots for 4 days.
If you're flying in, I would recommend using Lauda Air, which is one of the best carriers my wife and I have encountered in years. Founded by Austrian race driver and entrepreneur, Nicki Lauda, this is a class act. We flew them to and from Amsterdam, and on this relatively short, hour-and-fifty-minute flight, we were treated to wonderful food on real china, which we haven't seen outside business class in years. (See accompanying photo.) The seats, by the way, are goat-hide.
The staff is well-trained, friendly, and highly efficient. The only glitch was the insistance that a largish carry-on bag be checked, a bag we had happily carried on with us -- at a similar size and weight -- on many previous flights.
The airline serves most major European airports, North America, SE Asia, and the Far East.
We went there by plane from Brussel (Belgium). Was perfect. We had Lauda Air. This company is really nice. We got our food from porcelain in stead of plastic!
We travelled around by metro. This is always a very convenient way to travel, but in Vienna i felt save in the metro (this i cannot say everywhere)
You can get by plane to Vienna International Airport (19 km from the city centre). It can also be easily reached by the train, to Sûdbahnhof or Westbahnhof.