From the airport take the ÖBB train S7 direction "Wien Floridsdorf" or train S2 direction "Laa/Thaya Bahnhof" until "Wien-Mitte Landstraße".
From "Wien-Mitte Landstrasse" take the metro line U4 (green line) direction "Hütteldorf" until the stop "Schönbrunn" (Metro Exit "Grünbergstraße"), then a 3-minutes walk to the venue.
You can buy tickets for the train directly at vending machines on the platform. Choose "Schönbrunn" as destination. You will pay around 5 to 6 EUR (2,40 for the train, about 3 for the metro).
The "City Airport Train" (CAT) which also goes to "Wien-Mitte Landstraße" is a couple of minutes faster but costs just for the train (no metro) around 11 EUR.
There is no train service in the night hours between 00:00 and 5:00, if you arrive late you can take the bus "Vienna Airport Lines" and get out at "Schwedenplatz". From there you can also change to the metro line U4 until "Schönbrunn"