S2 train station is located near the first terminal. Follow the signs for the S2 train station. The train leaves every 20 minutes. One trip costs about five euros. The journey takes about half an hour. There is also a direct train from the airport to the city, the ticket costs twice as much, the duration of the journey is twice as fast. The direct train is green colored and easy to recognize by the gray-green CAT logo (City Airport Train). You need to go to the Vienna Mitte stop.
Photo: By Linie29 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=49097731