by Plane

Vienna has an international airport (VIE) situated in the south of the city. Once you are there the easiest way to reach the city is to take a train from the airport train station. Alternatively, you can take taxis from the airport. 

• The Railjet trains of the Austrian train network ÖBB towards the main train station of Vienna (Wien HBF). It takes about 15 minutes and costs 4.40 Euro. It runs every half hour.
• Tram S7 towards Floridsdorf takes about 25 minutes to reach the station “Wien Mitte”, where you can switch to the subway system and costs 4.30 Euro. Runs every half hour too. From there you can just get into the local transportation system of the “Wiener Linien” (to subway (U-Bahn), tram (Straßenbahn), local bus (Bus)). 
• The CAT airport train costs 14.90 Euro and runs to “Wien Mitte” in about 16 minutes. From there you can just get into the the local transportation system of the “Wiener Linien” (to subway (U-Bahn), tram (Straßenbahn), local bus (Bus)).
• An airport taxi for one person should costs you about 42-50 EUR for a drive from the airport to the city center. From there you can just get into the local transportation system of the “Wiener Linien” (to subway (U-Bahn), tram (Straßenbahn), local bus (Bus)).

by Train

In case you arrive to Vienna via train you will most likely exit at the main train station  - Wien Hauptbahnhof (Wien HBF), just south of the city center. From there you can just get into the local transportation system of the “Wiener Linien” (to subway (U-Bahn), tram (Straßenbahn), local bus (Bus)).

by Car

Vienna has a rather bad parking in the center. In case you are traveling by car we highly recommend to leave it in one of the “park+ride” P+R garages (an overview can be found here and here). From there you can just get into the local transportation system of the “Wiener Linien” (to subway (U-Bahn), tram (Straßenbahn), local bus (Bus)).