By bus: Buses from Vienna International Airport to Wien Meidling train station operate between 5:10 and 23:10, every 30 minutes, and a single ticket for one way costs 8 Euro (timetable is here). You should take the bus 1187 in direction of Westbanhof and leave it on the first stop Wien Meidling (in about 15 minutes). The tickets are sold by the driver.

By taxi: Taxis from Vienna airport to Wien Meidling train station cost around 35 Euro (and there might be an extra charge for luggage). Duration of trip: 20 Min (longer during rush hours).

By train: Duration of trip about 2h40min. The price for the ticket Vienna-Graz (one way) is 37 Euro. Departures: You have a connection from Wien Meidling to Graz hourly from 6:03 till 21:03 (i.e, at 6:03, 7:03, 8:03, ..., 20:03, 21:03).

Note: As the train climbs Semmering mountain, you will have a beautiful view on the left side (going from Vienna to Graz).

Cost: (by public transportation - train or bus): 2 Euro.
This is just one zone in Graz's public transportation system. The one-hour ticket that you buy for the train or bus at the airport is valid for the whole ride from the airport to any destination in Graz, using any combination of trams, buses, etc.

By bus: Bus line 630 stops right in front of the main exit of the airport and goes to Jakominiplatz. Duration of trip: about 20 Min.

By train: The train station is about 300m outside the airport, and is visible from the airport's main exit. Duration of trip: 9 Min. There are trains to Graz Hauptbahnhof every hour.

By taxi: A taxi from Graz Thalerhof airport to the center of Graz (or near the Technical University, where the conference will take place) should cost about Euro 20, no extra charge for luggage.

By train: Duration of trip about 2h40min. The price for the ticket Vienna-Graz (one way) is 37 Euro. Departures: You have a connection from Graz to Wien Meidling every hour from 6:25 till 20:25 (6:25 (not on Sundays), 7:25, 8:25,..., 20:25). An extra train is at 5:37 every day.