We recommend to take a taxi, which are available directly in front of the airport building. The fare from the airport to the institute will cost approximately €20 and will take about 20 minutes to arrive.
If you arrive at Graz Main station you can take a taxi; or you can take tram line 6 (towards St. Peter) and get off at stop St. Peter Schulzentrum. At the side of the street (Petersgasse) is a sign saying "Technische Universität Graz - Bereich Inffeldgasse", pointing down Inffeldgasse. Follow that sign until you see the first university building (Studienzentrum Informatik) on the right hand side. Turn right after that building, the institute is located in the gray building right in front of you, on the first floor.