car:

From North / Vienna and East: on the A2 Südautobahn
From North and West: on the A9 Phyrnautobahn
From South / Klagenfurt and Italy: on the A2 autobahn
From South / Maribor: on the A9 autobahn

train:

Intercity trains connect Graz with all bigger towns of Austria. Direct train connections to some neighboring countries. Main changing stations: Salzburg and Bischofshofen coming form the North and Villach coming from the South.

airplane:

Graz Thalerhof, phone: +43 316 2915410
Connections to all major airports; main airlines: Lufthansa, Austrian Airlines and Tyrolean Airways.