Travelling from the airport to the city

Vienna Airport is situated right outside the city and is a relatively small airport. You can shop in about 30 taxfree shops, but don't expect any bargains. Most products cost about 3 euro more compared to the prices in the city (cd's, liquer etc).

The cheapest way to get from the airport to the city is taking the S-bahn. Both S7 and S8 (which isn't listed in any of the transport maps) take you to the central (subway)station in Vienna in about 35 minutes. Costs: EUR 1,70 (with Vienna Card) or EUR 3,70 (without Vienna Card).
The only hard part is finding the entrance of the S-bahn station if you're not familiair with the pictograms: look for the trainsymbol with the red S in the upper left corner!

The alternative is taking a cab (haven't tried that) or taking the City Express (CAT-train). Which costs a lot more and saves about 10 minutes...

Public transport is very extensively available in the city. Trams, busses, subwaytrains, they cover almost every part of Vienna. With a Vienna card you have unlimited excess for 72 hours. Just punch your card in a ticketmachine the moment you intent to start your first journey and it's all yours! Vienna cards are available at most shops and cost EUR 18,50 for 72 hours.