Vienna has a very good public transport system, which includes rail, commuter rail (S-Bahn), underground (U-Bahn), trams, and buses. The underground is very efficient and will take you to within a few minutes walk of anywhere you are likely to want to visit. The subway alone has the second highest per-capita ridership in the world.
You must validate (stamp) your ticket if the time and date is not printed on it before entering the subway platform or train or as soon as you get on a bus or tram. You do not need to show your ticket to the bus or tram operator.
Tickets are available at machines (Visa, MC accepted) and from counters at subway and rail stations as well as at tabacco shops (Tabak “Trafik”).
Although there are not many spot checks, the fine for travelling without a ticket is €100.