Vienna is a major European hub for trains, and is one of the largest stations in Europe. Trains from all over Europe arrive here every day, and this is probably the easiest way to arrive in Vienna from a city on the continent. Bratislava is only 30 minutes away by train, and Budapest only about 2.5 hours. Trains to Prague and Munich are a little longer at around 5 hours.
Vienna has three main train stations, South train station (Südbahnhof), Central Station (Wien Mitte) and West train station (Westbahnhof). Any of these stations provide good access to the city.
Vienna International Airport is located 19km to the south of the city, in the town of Schwechat. The airport is the hub city of Austria's national airline, and as such direct flights can be booked from hundreds of destinations.
In addition to Austrian Airlines, a number of European budget airlines including Niki, Air Berlin and easyJet.
You have a number of options for getting from the airport to the city center. The cheapest is just taking the local S-Bahn into the city. The journey lasts about 25 minutes, and a single ticket costs €3.40 (2 zone ticket). You can also buy a day ticket here, so that you can continue to use the Vienna public transport network for the whole day (or multiple days, depending on your ticket).
When you arrive, you will notice a lot of advertising for the CAT. This is a high speed train that will get you to the center of Vienna about 10 minutes quicker than the S-Bahn. This ticket however is more expensive, at €9. Using this service, you can also check your bags in at Wien-Mitte before the train departs, which can make your journey a little lighter.
There are also two different buses that leave from the airport. One goes from the airport to Südbahnhof and then onto Westbahnhof. The other line goes from the airport to Morinplatz, which is very close to the downtown center. Both trips cost €6, and tickets can be bought from the driver.
The easiest, but not the cheapest way, is to take a cab. A trip to the city center will cost between €25 and €50 depending on your destination.
Austria is a small country, and it seems that all roads lead to Vienna! Most highways terminate in Vienna, including the A1, Austria's main autobahn. If you intend to drive to the city, make sure you have purchased a Vignette (which costs around €7 for 10 days), or you could get a nasty fine.