Vienna has a good public transport system web, which includes rail, commuter rail, underground, trams (trolleys), 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, and that is not accounting for the 27 tram lines, dozens of train lines or numerous buses.
Public transportation with-in the city proper, including most everywhere you are likely to visit (the entire subway and tram network) is a single zone (Kernzone 100). Any transportation can be used: subway, any train--even high-speed ones--as long as you are traveling between two Vienna stations, trams, buses, night buses, and an inter-urban railway (the Wiener Lokalbahn) with-in the city limits.
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. Although there are not many spot checks, the fee for traveling without a ticket is €100.
Tickets are available at machines (Visa, MC accepted) and from counters at subway and rail stations as well as at tabacco shops (Tabak "Trafik").
If you are staying for a few days and hope to do tons of sightseeing and/or shopping, the Vienna Card (Wien Karte) web is a good deal. It costs €19.90 and is good for 72 hours of unlimited public transit within Vienna. The card also gets you discounts (typically €1 or €2 at the major museums and art galleries) to many attractions and shops. You can buy it at the airport, hotels, and underground stops.
The best rail (heavy rail and underground) transport map web is displayed at all ÖBB stations. There are so many lines that maps are normally very simplified, and there are no maps of the tram network. It can pay to ask or check the best connection ahead of time web. Major stations are well signed and connections are scheduled to match-up if service isn't frequent.
Vienna's suburban rail network is often overlooked by tourists. It comprises three types of trains: S-Bahn, which mostly serve inner suburbs and stop at all stations with few exceptions,Regionalbahn, which are generally more long-distant than the S-Bahn and make limited stops on parallell S-Bahn routes, but otherwise all stops, and RegionalExpress, which mostly serve the outermost suburbs and make very limited stops in the inner suburbs (although not all RegionalExpress trains are suburban trains). The network also stretches over the borders of the neighbouring countries.
The most important rail streches:
The five U-bahn lines (i.e. U1) are the most common way of getting around Vienna. These underground, metro or subway lines have trains every 2-7 minutes and cover most of the important parts of the city and sights.
Tram (Bim, Straßenbahn) lines have just a plain number or letter (O,1). There are 27 lines which stop locally, useful for taking things a bit slower and seing more of the city.
The famous Ring lines were recently changed: there is a tourist tram web around the ring, or you can take tram 1 (bound for Prater-Hauptalle) from Oper to Schwedenplatz and take tram 2 (bound for Ottakring) from Schwedenplatz back to Oper.
The Wiener Lokalbahn (WLB) also referred to as the Badner-Bahn is an interurban railway traveling from the Opera running as a tram on-street southwest through Vienna to Meidling station where it becomes a railway continuing onwards through the 23rd District and through suburbs and the rolling wine hills in Lower Austria to Baden.
Bus lines are denoted by a number that ends in letter (i.e. 3A, 80B). You are unlikely to need to take a bus, but it is safe to assume if you see one that you can get on and it will take you to some higher form of transportation like the U-Bahn. Cheaper tickets (€1) are available for most 'B' buses; regular tickets and passes are also valid.
The regular trams, trains and buses run until about 00:30 (just past midnight). Most of the commuter rail is shut between 1 AM and 4 AM. On Friday and Saturday (as well as on nights before holidays), the entire U-Bahn network runs all night. Additionally, a dense network of night buses, called "NightLiners" is available every night of the year. Regular tickets are valid. Most buses terminate at "Kärntner Ring, Oper", which allows for easy interchange. Intervals are every 15-30 min. Daytime service resumes at 5 AM.
Taxis are plentiful and can normally be hailed on the street or found at a taxi stand. Fares are set to a meter price, but if you prefer, you can always negotiate a fare. Always negotiate when traveling to the airport or outside of the city limits as fares are not set to those places. Pedicabs, horse-drawn coaches and the like are also available.
Avoid driving a car within the central ring if possible. While cars are allowed on many of the streets there, the streets are narrow and mostly one-way. They can be confusing for a visitor and parking is extremely limited (and restricted during the day). Due to the comprehensiveness of the transit system, you most likely will not need a car within Vienna, except for excursions elsewhere.
Furthermore, it might be a good idea to leave your car at home during rush hours. Vienna's streets can become a little clogged in the mornings and early evenings and the drivers are not really known for being especially polite and friendly.
Pedestrians have the right of way in crossing all roads at a crosswalk where there is no pedestrian signal present. If there is such a pedestrian crossing on an otherwise straight section of the road, there will be a warning sign: you are required to yield to any pedestrian on this crossing. Austrians accustomed to experienced local drivers will step out with little thought and force you to stop, so slow down here and be careful. When driving in a neighborhood this "right of way to pedestrians" is an understood rule at every intersection, although pedestrians will be more careful before they step out. Again, be on the lookout for this: if you see a pedestrian waiting to cross, you should stop at the intersection for him or her.
Cycling is another option for travelling within Vienna, although it is still seen more as a leisure activity in Vienna. web Vienna's compact size makes cycling attractive. On a bicycle you can reach most places of interest within half an hour. There are many bicycle paths and lanes along major streets, in parks, and by the rivers. However, it can be complicated to cross town because the lanes follow illogical routes. One major complaint is that bicycle facilites were an afterthought and this is very appearant, many stop lights and intersections are dangerously or annoyingly set for bicyclists and paths are very illogical: they are sometimes on-street sometimes off, sometimes shared with pedestrians, sometimes not, and can vary or end out of nowhere. You are required by law to use a bike lane or path if there is one, unless it is blocked, otherwise regular traffic laws apply. Lights are required at night as are independently functioning brakes.
If your destination is in the outer suburbs, or you want to take a relaxed ride to the countryside, you may consider taking your bike on the U-Bahn (prohibited at rush hour, and always in buses and trams) or on a train. You need a reduced (children's) ticket for your bike.
Walking can also be very pleasant. The inner ring is quite compact with lots of pleasant cobblestoned and paved streets. It can be crossed in about 20 min.
Bring a comfortable pair of walking shoes as this is the most common way of getting around.