The most simple way: take a taxi. It takes you about 20 minutes, approximate fare € 25. If you are travelling light you could consider going by public transport. Trains (commuter train S5) depart to the main station, from there you take any tram to the centre. Exit at stop ‘Hauptplatz/Congress’.
Buses (630/631) will take you to Jakominiplatz, from there it is one stop by tram or a 5-minutes walk. Check the time table
(from/von Graz, Flughafen Graz; to/nach Graz, Hauptplatz/Congress)