The Vienna Card   is the best way to take advantage of the extensive network of subway trains (which run till shortly after midnight), streetcars and buses.
Besides the ViennaCard, the following tickets are available:

• 24-hour season ticket 5.70 Euro
• 48-hour season ticket 10.- Euro
• 72-hour season ticket 13.60 Euro
• Single ride tickets 1.80 Euro

These tickets are available at the ticket sales offices of the Vienna Transport Authority, at tobacconists and from vending machines in the underground stations; the 72-hour season ticket is also available in the Tourist Information Office (1., Albertinaplatz, daily 9 am - 7 pm).
Single tickets are also available from the vending machines in the vehicles themselves (including single-ticket surcharge altogether 2,20 Euro, have coins ready!).
The ticket sales offices of the Vienna Transport Authority (Wiener Linien) can also provide information about other forms of ticket and sell a map of the public transport network.
Children under six always travel free, children under 15 on Sundays and public holidays and during the Viennese school holidays (identity card as proof of age!). There are reasonably priced "two-trip tickets for seniors" for women over 60 and men over 65 (passport or ID required) - purchase your ticket before you set off from a tobacconist or any ticket machine in a subway station.

Further information on Vienna Public Transport

Map of the public transport system (provided by "Wiener Linien")