The fastest would be to take an Intercity train from Vienna airport to Vienna Hbf. Cost is between 3 and 4 Euro (forgot the exact amount). There's a train something like every 15 minutes. Buy ticket from a machine, the line may be long.

There is also a CAT train, but it makes no sense if you have no/little luggage, because it takes the same time, while costing over 10 Euro.

At Vienna Hbf you jump into Metro (U1 line), and go three (or four?) stations north. to Stephansplatz, which is also on U1.

The fastest would be to take an Intercity train from Vienna airport to Vienna Hbf. Cost is between 3 and 4 Euro (forgot the exact amount). There's a train something like every 15 minutes. Buy ticket from a machine, the line may be long.

There is also a CAT train, but it makes no sense if you have no/little luggage, because it takes the same time, while costing over 10 Euro.

At Vienna Hbf you jump into Metro (U1 line), and go three (or four?) stations north. to Stephansplatz, which is also on U1.

Don't use Google Maps for navigation, it seems not to know about U lines (only S lines).